Quantum states of matter
Chiral spin states

• Wen, X. G., Wilczek, F. & Zee, A. Chiral spin states and superconductivity. Phys. Rev. B 39, 11413–11423 (1989).

Topological orders

• Chen, X., Gu, Z.-C., Liu, Z.-X. & Wen, X.-G. Symmetry-Protected Topological Orders in Interacting Bosonic Systems. Science 338, 1604–1606 (2012).
• Benalcazar, W. A., Bernevig, B. A. & Hughes, T. L. Quantized electric multipole insulators. Science 357, 61–66 (2017).
• Imhof, S. et al. Topolectrical-circuit realization of topological corner modes. Nat. Phys. 14, 925–929 (2018). [R. Thomale]

Valence-bond states

• Anderson, P. W. Resonating valence bonds: A new kind of insulator? Mater. Res. Bull. 8, 153–160 (1972).
• Anderson, P. W. The Resonating Valence Bond State in La₂CuO₄ and Superconductivity. Science 235, 1196–1198 (1987).
• Affleck, I., Kennedy, T., Lieb, E. H. & Tasaki, H. Rigorous results on valence-bond ground states in antiferromagnets. Phys. Rev. Lett. 59, 799–802 (1987).
• Kalmeyer, V. & Laughlin, R. B. Equivalence of the resonating-valence-bond and fractional quantum Hall states. Phys. Rev. Lett. 59, 2095–2098 (1987).

Anyons

• Wilczek, F. Quantum Mechanics of Fractional-Spin Particles. Phys. Rev. Lett. 49, 957–959 (1982).
• Kitaev, A. Anyons in an exactly solved model and beyond. Ann. Phys. 321, 2–111 (2006).
• Bartolomei, H. et al. Fractional statistics in anyon collisions. Science 368, 6487 (2020). [G. Fève]
• Nakamura, J., Liang, S., Gardner, G. C. & Manfra, M. J. Direct observation of anyonic braiding statistics. Nat. Phys. 16, 931–936 (2020).

Levitons

• Dubois, J. et al. Minimal-excitation states for electron quantum optics using levitons. Nature 502, 659–663 (2013). [DC. Glattli]

Band topology

• Sundaram, G. & Niu, Q. Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects. Phys. Rev. B 59, 14915–14925 (1999).
• Pesin, D. & Balents, L. Mott physics and band topology in materials with strong spin–orbit interaction. Nat. Phys. 6, 376–381 (2010).
• Parameswaran, S. A., Grover, T., Abanin, D. A., Pesin, D. A. & Vishwanath, A. Probing the Chiral Anomaly with Nonlocal Transport in Three-Dimensional Topological Semimetals. Phys. Rev. X 4, 031035 (2014).
• Bradlyn, B. et al. Topological quantum chemistry. Nature 547, 298–305 (2017). [BA. Bernevig]
• Gianfrate, A. et al. Measurement of the quantum geometric tensor and of the anomalous Hall drift. Nature 578, 381–385 (2020). [D. Sanvitto/G. Malpuech]

Hubbard model

• Jiang, H.-C. & Devereaux, T. P. Superconductivity in the doped Hubbard model and its interplay with next-nearest hopping t′. Science 365, 1424–1428 (2019).

Phase transitions

• Senthil, T., Vishwanath, A., Balents, L., Sachdev, S. & Fisher, M. P. A. Deconfined Quantum Critical Points. Science 303, 1490–1494 (2004).

Sachdev-Ye-Kitaev model

• Gu, Y., Kitaev, A., Sachdev, S. & Tarnopolsky, G. Notes on the complex Sachdev-Ye-Kitaev model. J. High Energ. Phys. 2020, 157 (2020).

Hall effects
Quantum Hall effect

• Laughlin, R. B. Quantized Hall conductivity in two dimensions. Phys. Rev. B 23, 5632–5633 (1981).
• Halperin, B. I. Quantized Hall conductance, current-carrying edge states, and the existence of extended states in a two-dimensional disordered potential. Phys. Rev. B 25, 2185–2190 (1982).
• Chklovskii, D. B., Shklovskii, B. I. & Glazman, L. I. Electrostatics of edge channels. Phys. Rev. B 46, 4026–4034 (1992).

Fractional quantum Hall effect

• Laughlin, R. B. Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations. Phys. Rev. Lett. 50, 1395–1398 (1983).
• Arovas, D., Schrieffer, J. R. & Wilczek, F. Fractional Statistics and the Quantum Hall Effect. Phys. Rev. Lett. 53, 722–723 (1984).
• Jain, J. K. Composite-fermion approach for the fractional quantum Hall effect. Phys. Rev. Lett. 63, 199–202 (1989).

Quantum anomalous Hall effect

• Haldane, F. D. M. Model for a Quantum Hall Effect without Landau Levels: Condensed-Matter Realization of the ‘Parity Anomaly’. Phys. Rev. Lett. 61, 2015–2018 (1988).

Quantum spin Hall effect

• Kane, C. L. & Mele, E. J. Z₂ Topological Order and the Quantum Spin Hall Effect. Phys. Rev. Lett. 95, 146802 (2005).
• Kane, C. L. & Mele, E. J. Quantum Spin Hall Effect in Graphene. Phys. Rev. Lett. 95, 226801 (2005).
• Qi, X.-L., Wu, Y.-S. & Zhang, S.-C. Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors. Phys. Rev. B 74, 085308 (2006).

Quantum nonlinear Hall effect

• Sodemann, I. & Fu, L. Quantum Nonlinear Hall Effect Induced by Berry Curvature Dipole in Time-Reversal Invariant Materials. Phys. Rev. Lett. 115, 216806 (2015).

Magnon Hall effect

• Onose, Y. et al. Observation of the Magnon Hall Effect. Science 329, 297–299 (2010). [Y. Tokura]

Thermal Hall effect

• Katsura, H., Nagaosa, N. & Lee, P. A. Theory of the Thermal Hall Effect in Quantum Magnets. Phys. Rev. Lett. 104, 066403 (2010).

Topological databases

• Zhang, T. et al. Catalogue of topological electronic materials. Nature 566, 475–479 (2019). [HM. Wang/C. Fang]
• Vergniory, M. G. et al. A complete catalogue of high-quality topological materials. Nature 566, 480–485 (2019). [BA. Bernevig/ZJ. Wang]
• Tang, F., Po, H. C., Vishwanath, A. & Wan, X. Comprehensive search for topological materials using symmetry indicators. Nature 566, 486–489 (2019).
• Xu, Y. et al. High-throughput calculations of magnetic topological materials. Nature 586, 702–707 (2020). [BA. Bernevig]
• Vergniory, M. G. et al. All topological bands of all nonmagnetic stoichiometric materials. Science 376, eabg9094 (2022). [N. Regnault]

Topological insulators (TI)
Theory

• Fu, L., Kane, C. L. & Mele, E. J. Topological Insulators in Three Dimensions. Phys. Rev. Lett. 98, 106803 (2007).
• Fu, L. & Kane, C. L. Topological insulators with inversion symmetry. Phys. Rev. B 76, 045302 (2007).

Bi₂Se₃

• Peng, H. et al. Aharonov–Bohm interference in topological insulator nanoribbons. Nat. Mater. 9, 225–229 (2009). [Y. Cui]
• Mellnik, A. R. et al. Spin-transfer torque generated by a topological insulator. Nature 511, 449–451 (2014). [DC. Ralph]
• Wu, L. et al. Quantized Faraday and Kerr rotation and axion electrodynamics of a 3D topological insulator. Science 354, 1124–1127 (2016). [NP. Armitage]

Bi₂Te₃

• Schmid, C. P. et al. Tunable non-integer high-harmonic generation in a topological insulator. Nature 593, 385–390 (2021). [J. Wilheim/K. Richter/R. Huber]

Cr-doped (Bi,Sb)₂Te₃

• Yu, R. et al. Quantized Anomalous Hall Effect in Magnetic Topological Insulators. Science 329, 61–64 (2010). [X. Dai/Z. Fang]
• Chang, C.-Z. et al. Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator. Science 340, 167–170 (2013). [K. He/YY. Wang/QK. Xue]
• Checkelsky, J. G. et al. Trajectory of the anomalous Hall effect towards the quantized state in a ferromagnetic topological insulator. Nat. Phys. 10, 731–736 (2014). [Y. Tokura]
• Zhao, Y.-F. et al. Tuning the Chern number in quantum anomalous Hall insulators. Nature 588, 419–423 (2020). [CX. Liu/CZ. Chang]

HgTe quantum wells

• König, M. et al. Quantum Spin Hall Insulator State in HgTe Quantum Wells. Science 318, 766–770 (2007). [SC. Zhang]
• Brüne, C. et al. Quantum Hall Effect from the Topological Surface States of Strained Bulk HgTe. Phys. Rev. Lett. 106, 126803 (2011). [LW. Molenkamp]
• Bocquillon, E. et al. Gapless Andreev bound states in the quantum spin Hall insulator HgTe. Nat. Nanotechnol. 12, 137–143 (2016). [LW. Molenkamp]
• Wiedenmann, J. et al. 4π-periodic Josephson supercurrent in HgTe-based topological Josephson junctions. Nat. Commun. 7, 1–7 (2016). [LW. Molenkamp]

Bi bilayers

• Drozdov, I. K. et al. One-dimensional topological edge states of bismuth bilayers. Nat. Phys. 10, 664–669 (2014). [A. Yazdani]

Topological crystalline insulators
Pb_1-xSn_xTe

• Xu, S.-Y. et al. Observation of a topological crystalline insulator phase and topological phase transition in Pb_1-xSn_xTe. Nat. Commun. 3, 1192 (2012). [MZ. Hasan]

Dirac semimetals (DSM)
Cd₃As₂

• Moll, P. J. W. et al. Transport evidence for Fermi-arc-mediated chirality transfer in the Dirac semimetal Cd₃As₂. Nature 535, 266–270 (2016). [JG. Analytis]
• Zhang, C. et al. Quantum Hall effect based on Weyl orbits in Cd₃As₂. Nature 565, 331–336 (2018). [FX. Xiu]

ZrTe₅

• Tang, F. et al. Three-dimensional quantum Hall effect and metal–insulator transition in ZrTe₅. Nature 569, 537 (2019). [ZH. Qiao/LY. Zhang]

Na₃Bi

• Xu, S.-Y. et al. Observation of Fermi arc surface states in a topological metal. Science 347, 294–298 (2014). [MZ. Hasan]
• Xiong, J. et al. Evidence for the chiral anomaly in the Dirac semimetal Na₃Bi. Science 350, 413–416 (2015). [NP. Ong]

Weyl semimetals (WSM)
Theory

• Nielsen, H. B. & Ninomiya, M. The Adler-Bell-Jackiw anomaly and Weyl fermions in a crystal. Phys. Lett. B 130, 389–396 (1983).
• Vazifeh, M. M. & Franz, M. Electromagnetic Response of Weyl Semimetals. Phys. Rev. Lett. 111, 027201 (2013).
• Son, D. T. & Spivak, B. Z. Chiral anomaly and classical negative magnetoresistance of Weyl metals. Phys. Rev. B 88, 104412 (2013).
• Potter, A. C., Kimchi, I. & Vishwanath, A. Quantum oscillations from surface Fermi arcs in Weyl and Dirac semimetals. Nat. Commun. 5, 5161 (2014).
• Zhao, B., Guo, C., Garcia, C. A. C., Narang, P. & Fan, S. Axion-Field-Enabled Nonreciprocal Thermal Radiation in Weyl Semimetals. Nano Lett. 20, 1923–1927 (2020).

TaAs/TaP/NbAs/NbP

• Weng, H., Fang, C., Fang, Z., Bernevig, B. A. & Dai, X. Weyl Semimetal Phase in Noncentrosymmetric Transition-Metal Monophosphides. Phys. Rev. X 5, 011029 (2015).
• Wu, L. et al. Giant anisotropic nonlinear optical response in transition metal monopnictide Weyl semimetals. Nat. Phys. 13, 350–355 (2016). [J. Orenstein]

TaAs

• Xu, S.-Y. et al. Discovery of a Weyl fermion semimetal and topological Fermi arcs. Science 349, 613–617 (2015). [MZ. Hasan]
• Lv, B. et al. Observation of Weyl nodes in TaAs. Nat. Phys. 11, 724–727 (2015). [T. Qian/M. Shi/H. Ding]
• Huang, S.-M. et al. A Weyl Fermion semimetal with surface Fermi arcs in the transition metal monopnictide TaAs class. Nat. Commun. 6, 7373 (2015). [H. Lin/MZ. Hasan]
• Lv, B. et al. Experimental Discovery of Weyl Semimetal TaAs. Phys. Rev. X 5, 031013 (2015). [T. Qian/H. Ding]
• Huang, X. et al. Observation of the Chiral-Anomaly-Induced Negative Magnetoresistance in 3D Weyl Semimetal TaAs. Phys. Rev. X 5, 031023 (2015). [GF. Chen]
• Zhang, C.-L. et al. Signatures of the Adler–Bell–Jackiw chiral anomaly in a Weyl fermion semimetal. Nat. Commun. 7, 10735 (2016). [MZ. Hasan/S. Jia]
• Ma, Q. et al. Direct optical detection of Weyl fermion chirality in a topological semimetal. Nat. Phys. 13, 842–847 (2017). [P. Jarillo-Herrero/N. Gedik]

TaP

• Liu, Z. K. et al. Evolution of the Fermi surface of Weyl semimetals in the transition metal pnictide family. Nat. Mater. 15, 27–31 (2015). [YL. Chen]
• Xu, S.-Y. et al. Experimental discovery of a topological Weyl semimetal state in TaP. Sci. Adv. 1, e1501092 (2015). [MZ. Hasan]
• Arnold, F. et al. Negative magnetoresistance without well-defined chirality in the Weyl semimetal TaP. Nat. Commun. 7, 11615 (2016). [E. Hassinger/BH. Yan]

NbP

• Shekhar, C. et al. Extremely large magnetoresistance and ultrahigh mobility in the topological Weyl semimetal candidate NbP. Nat. Phys. 11, 645–649 (2015). [BH. Yan]
• Liu, Z. K. et al. Evolution of the Fermi surface of Weyl semimetals in the transition metal pnictide family. Nat. Mater. 15, 27–31 (2015). [YL. Chen]
• Gooth, J. et al. Experimental signatures of the mixed axial–gravitational anomaly in the Weyl semimetal NbP. Nature 547, 324–327 (2017). [K. Nielsch]

(TaSe₄)₂I

• Gooth, J. et al. Axionic charge-density wave in the Weyl semimetal (TaSe₄)₂I. Nature 575, 315-319 (2019). [C. Felser]
• Shi, W. et al. A charge-density-wave topological semimetal. Nat. Phys. 17, 381–387 (2021). [BA. Bernevig/XJ. Wang]

TaIrTe₄

• Ma, J. et al. Nonlinear photoresponse of type-II Weyl semimetals. Nat. Mater. 18, 476–481 (2019). [JH. Chen/J. Feng/D. Sun]

Co₃Sn₂S₂

• Liu, E. et al. Giant anomalous Hall effect in a ferromagnetic kagome-lattice semimetal. Nat. Phys. 14, 1125–1131 (2018). [C. Felser]
• Wang, Q. et al. Large intrinsic anomalous Hall effect in half-metallic ferromagnet Co₃Sn₂S₂ with magnetic Weyl fermions. Nat. Commun. 9, 3681 (2018). [HM. Wang/SC. Wang/HC. Lei]
• Liu, D. F. et al. Magnetic Weyl semimetal phase in a Kagomé crystal. Science 365, 1282–1285 (2019). [YL. Chen]
• Morali, N. et al. Fermi-arc diversity on surface terminations of the magnetic Weyl semimetal Co₃Sn₂S₂. Science 365, 1286–1291 (2019). [H. Beidenkopf]
• Yin, J.-X. et al. Negative flat band magnetism in a spin–orbit-coupled correlated kagome magnet. Nat. Phys. 15, 443–448 (2019). [MZ. Hasan]
• Guin, S. N. et al. Zero-Field Nernst Effect in a Ferromagnetic Kagome-Lattice Weyl-Semimetal Co₃Sn₂S₂. Adv. Mater. 31, 1806622 (2019). [C. Felser]

Mn₃X

• Zhang, Y. et al. Strong anisotropic anomalous Hall effect and spin Hall effect in the chiral antiferromagnetic compounds Mn₃X (X=Ge, Sn, Ga, Ir, Rh, and Pt). Phys. Rev. B 95, 075128 (2017). [BH. Yan]

Mn₃Ge

• Yang, H. et al. Topological Weyl semimetals in the chiral antiferromagnetic materials Mn₃Ge and Mn₃Sn. New J. Phys. 19, 015008 (2017). [BH. Yan]

Mn₃Sn

• Nakatsuji, S., Kiyohara, N. & Higo, T. Large anomalous Hall effect in a non-collinear antiferromagnet at room temperature. Nature 527, 212–215 (2015). [T. Higo]
• Kuroda, K. et al. Evidence for magnetic Weyl fermions in a correlated metal. Nat. Mater. 16, 1090–1095 (2017). [S. Nakatsuji]
• Yang, H. et al. Topological Weyl semimetals in the chiral antiferromagnetic materials Mn₃Ge and Mn₃Sn. New J. Phys. 19, 015008 (2017). [BH. Yan]
• Tsai, H. et al. Electrical manipulation of a topological antiferromagnetic state. Nature 580, 608–613 (2020).
• Takeuchi, Y. et al. Chiral-spin rotation of non-collinear antiferromagnet by spin–orbit torque. Nat. Mater. 20, 1364–1370 (2021). [S. Fukami/H. Ohno]

YbMnBi₂

• Borisenko, S. et al. Time-reversal symmetry breaking type-II Weyl state in YbMnBi₂. Nat. Commun. 10, 3424 (2019). [RJ. Cava]

SrSi₂

• Huang, S.-M. et al. New type of Weyl semimetal with quadratic double Weyl fermions. PNAS 113, 1180–1185 (2016). [H. Lin/MZ. Hasan]

GdPtBi

• Suzuki, T. et al. Large anomalous Hall effect in a half-Heusler antiferromagnet. Nat. Phys. 12, 1119–1123 (2016). [JG. Checkelsky]

Nodal-line semimetals
Co₂MnGa

• Sakai, A. et al. Giant anomalous Nernst effect and quantum-critical scaling in a ferromagnetic semimetal. Nat. Phys. 14, 1119–1124 (2018). [S. Nakatsuji]
• Belopolski, I. et al. Discovery of topological Weyl fermion lines and drumhead surface states in a room temperature magnet. Science 365, 1278–1281 (2019). [MZ. Hasan]
• Guin, S. N. et al. Anomalous Nernst effect beyond the magnetization scaling relation in the ferromagnetic Heusler compound Co₂MnGa. NPG Asia Mater. 11, 16 (2019) [J. Gooth/C. Felser]

Co₂MnAl

• Li, P. et al. Giant room temperature anomalous Hall effect and tunable topology in a ferromagnetic topological semimetal Co₂MnAl. Nat. Commun. 11, 3476 (2020). [ZQ. Mao/BH. Yan]

Kagomé
CoSn

• Liu, Z. et al. Orbital-selective Dirac fermions and extremely flat bands in frustrated kagome-lattice metal CoSn. Nat. Commun. 11, 4002 (2020). [ZP. Yin/HC. Lei/SC. Wang]
• Kang, M. et al. Topological flat bands in frustrated kagome lattice CoSn. Nat. Commun. 11, 4004 (2020). [R. Comin]

FeSn

• Kang, M. et al. Dirac fermions and flat bands in the ideal kagome metal FeSn. Nat. Mater. 19, 163-169 (2019). [JG. Checkelsky/R. Comin]

Fe₃Sn₂

• Ye, L. et al. Massive Dirac fermions in a ferromagnetic kagome metal. Nature 555, 638–642 (2018). [R. Comin/JG. Checkesky]
• Yin, J.-X. et al. Giant and anisotropic many-body spin–orbit tunability in a strongly correlated kagome magnet. Nature 562, 91–95 (2018). [MZ. Hasan]

TbMn₆Sn₆

• Yin, J.-X. et al. Quantum-limit Chern topological magnetism in TbMn₆Sn₆. Nature 583, 533–536 (2020). [S. Jia/MZ. Hasan]

YMn₆Sn₆

• Ghimire, N. J. et al. Competing magnetic phases and fluctuation-driven scalar spin chirality in the kagome metal YMn₆Sn₆. Sci. Adv. 6, eabe2680 (2020). [II. Mazin]

AV₃Sb₅ (A = Cs, K, Rb)

• Ortiz, B. R. et al. New kagome prototype materials: discovery of KV₃Sb₅, RbV₃Sb₅, and CsV₃Sb₅. Phys. Rev. Mater. 3, 094407 (2019). [ES. Toberer]
• Li, H. et al. Observation of Unconventional Charge Density Wave without Acoustic Phonon Anomaly in Kagome Superconductors AV₃Sb₅ (A=Rb, Cs). Phys. Rev. X 11, 031050 (2021). [H. Miao]
• Tan, H., Liu, Y., Wang, Z. & Yan, B. Charge Density Waves and Electronic Properties of Superconducting Kagome Metals. Phys. Rev. Lett. 127, 046401 (2021).
• Feng, X., Jiang, K., Wang, Z. & Hu, J. Chiral flux phase in the Kagome superconductor AV₃Sb₅. Sci. Bull. 66, 1384-1388 (2021).

CsV₃Sb₅

• Ortiz, B. R. et al. CsV₃Sb₅: A Z₂ Topological Kagome Metal with a Superconducting Ground State. Phys. Rev. Lett. 125, 247002 (2020). [SD. Wilson]
• Zhao, H. et al. Cascade of correlated electron states in a kagome superconductor CsV₃Sb₅. Nature 599, 216-221 (2021). [I. Zelkovic]
• Chen, H. et al. Roton pair density wave in a strong-coupling kagome superconductor. Nature 599, 222-228 (2021). [ZQ. Wang/HJ. Gao]
• Liang, Z. et al. Three-Dimensional Charge Density Wave and Surface-Dependent Vortex-Core States in a Kagome Superconductor CsV₃Sb₅. Phys. Rev. X 11, 031026 (2021). [L. Shan/ZY. Wang/XH. Chen]
• Chen, K. Y. et al. Double Superconducting Dome and Triple Enhancement of T_c in the Kagome Superconductor CsV₃Sb₅ under High Pressure. Phys. Rev. Lett. 126, 247001 (2021). [JP. Sun/HC. Lei/JP. Hu/JG. Cheng]
• Zhang, Z. et al. Pressure-induced reemergence of superconductivity in the topological kagome metal CsV₃Sb₅. Phys. Rev. B 103, 224513 (2021). [XL. Chen/JH. Zhou/ZR. Yang]
• Yu, F. H. et al. Concurrence of anomalous Hall effect and charge density wave in a superconducting topological kagome metal. Phys. Rev. B 104, L041103 (2021). [JJ. Ying/XH. Chen]
• Chen, X. et al. Highly Robust Reentrant Superconductivity in CsV₃Sb₅ under Pressure. Chin. Phys. Lett. 38, 057402 (2021). [XL. Chen]
• Ni, S. et al. Anisotropic Superconducting Properties of Kagome Metal CsV₃Sb₅. Chin. Phys. Lett. 38, 057403 (2021). [ZX. Zhao]
• Duan, W. et al. Nodeless superconductivity in the kagome metal CsV₃Sb₅. Sci. China Phys. Mech. Astron. 64, 107462 (2021). [Y. Song/HQ. Yuan]
• Guo, C. et al. Switchable chiral transport in charge-ordered kagome metal CsV₃Sb₅. Nature 611, 461–466 (2022). [PJW. Moll]

KV₃Sb₅

• Yang, S.-Y. et al. Giant, unconventional anomalous Hall effect in the metallic frustrated magnet candidate, KV₃Sb₅. Sci. Adv. 6, eabb6003 (2020). [MN. Ali]
• Jiang, Y.-X. et al. Unconventional chiral charge order in kagome superconductor KV₃Sb₅. Nat. Mater. 20, 1353-1357 (2021). [MZ. Hasan]
• Du, F. et al. Pressure-induced double superconducting domes and charge instability in the kagome metal KV₃Sb₅. Phys. Rev. B 103, L220504 (2021). [Y. Song/HQ. Yuan]
• Ortiz, B. R. et al. Superconductivity in the Z₂ kagome metal KV₃Sb₅. Phys. Rev. Mater. 5, 034801 (2021). [SD. Wilson]
• Kenney, E. M., Ortiz, B. R., Wang, C., Wilson, S. D. & Graf, M. Absence of local moments in the kagome metal KV₃Sb₅ as determined by muon spin spectroscopy. J. Phys. Condens. Matter. 33, 235801 (2021).
• Li, H. et al. Rotation symmetry breaking in the normal state of a kagome superconductor KV₃Sb₅. Nat. Phys. 18, 265-270 (2022). [I. Zeljkovic]

RbV₃Sb₅

• Yin, Q. et al. Superconductivity and Normal-State Properties of Kagome Metal RbV₃Sb₅ Single Crystals. Chin. Phys. Lett. 38, 037403 (2021). [HC. Lei]

Chiral
XSi (X = Co, Rh)

• Sanchez, D. S. et al. Topological chiral crystals with helicoid-arc quantum states. Nature 567, 500–505 (2019).

CoSi

• Rao, Z. et al. Observation of unconventional chiral fermions with long Fermi arcs in CoSi. Nature 567, 496–499 (2019). [HC. Lei/YJ. Sun/T. Qian/H. Ding]
• Takane, D. et al. Observation of Chiral Fermions with a Large Topological Charge and Associated Fermi-Arc Surface States in CoSi. Phys. Rev. Lett. 122, 076402 (2019). [T. Sato]

RhSi

• Chang, G. et al. Unconventional Chiral Fermions and Large Topological Fermi Arcs in RhSi. Phys. Rev. Lett. 119, 206401 (2017). [H. Lin/MZ. Hasan]
• Rees, D. et al. Helicity-dependent photocurrents in the chiral Weyl semimetal RhSi. Sci. Adv. 6, eaba0509 (2020). [DH. Torchinsky/J. Orenstein]

Polar materials
BiTeI

• Ishizaka, K. et al. Giant Rashba-type spin splitting in bulk BiTeI. Nat. Mater. 10, 521–526 (2011). [Y. Tokura]

Skyrmions
Gd₃Ru₄Al₁₂

• Hirschberger, M. et al. Skyrmion phase and competing magnetic orders on a breathing kagomé lattice. Nat. Commun. 10, 5831 (2019). [Y. Tokura]

Gd₂PdSi₃

• Kurumaji, T. et al. Skyrmion lattice with a giant topological Hall effect in a frustrated triangular-lattice magnet. Science 365, 914–918 (2019). [Y. Tokura]

Synthetic

• Legrand, W. et al. Room-temperature stabilization of antiferromagnetic skyrmions in synthetic antiferromagnets. Nat. Mater. 19, 34-42 (2019). [V. Cros/A. Fert]

Quantum spin liquids
α-RuCl₃

• Banerjee, A. et al. Neutron scattering in the proximate quantum spin liquid α-RuCl₃. Science 356, 1055–1059 (2017). [SE. Nagler]
• Kasahara, Y. et al. Majorana quantization and half-integer thermal quantum Hall effect in a Kitaev spin liquid. Nature 559, 227-231 (2018). [Y. Matsuda]
• Banerjee, A. et al. Excitations in the field-induced quantum spin liquid state of α-RuCl₃. npj Quantum Mater. 3, 8 (2018). [SE. Nagler]
• Yokoi, T. et al. Half-integer quantized anomalous thermal Hall effect in the Kitaev material candidate α-RuCl₃. Science 373, 568–572 (2021). [Y. Matsuda]
• Czajka, P. et al. Oscillations of the thermal conductivity in the spin-liquid state of α-RuCl₃. Nat. Phys. 17, 915–919 (2021). [NP. Ong]
• Czajka, P. et al. Planar thermal Hall effect of topological bosons in the Kitaev magnet α-RuCl₃. Nat. Mater. 22, 36–41 (2023). [NP. Ong]

YbMgGaO₄

• Shen, Y. et al. Evidence for a spinon Fermi surface in a triangular-lattice quantum-spin-liquid candidate. Nature 540, 559–562 (2016). [G. Chen/J. Zhao]

ZnCu₃(OD)₆Cl₂ (herbertsmithite)

• Han, T.-H. et al. Fractionalized excitations in the spin-liquid state of a kagome-lattice antiferromagnet. Nature 492, 406–410 (2012). [YS. Lee]

Superconductors
UTe₂

• Ran, S. et al. Nearly ferromagnetic spin-triplet superconductivity. Science 365, 684–687 (2019). [NP. Butch]
• Ran, S. et al. Extreme magnetic field-boosted superconductivity. Nat. Phys. 15, 1250-1254 (2019). [NP. Butch]
• Jiao, L. et al. Chiral superconductivity in heavy-fermion metal UTe₂. Nature 579, 523–527 (2020). [V. Madhavan]

CeRh₂As₂

• Khim, S. et al. Field-induced transition within the superconducting state of CeRh₂As₂. Science 373, 1012–1016 (2021). [E. Hassinger]

Cuprates

• Bednorz, J. G. & Müller, K. A. Possible high T_c superconductivity in the Ba−La−Cu−O system. Z. Physik B 64, 189–193 (1986).
• Ozyuzer, L. et al. Emission of Coherent THz Radiation from Superconductors. Science 318, 1291–1293 (2007). [U. Welp]
• da Silva Neto, E. H. et al. Ubiquitous Interplay Between Charge Ordering and High-Temperature Superconductivity in Cuprates. Science 343, 393–396 (2013). [A. Yazdani]
• Božović, I., He, X., Wu, J. & Bollinger, A. T. Dependence of the critical temperature in overdoped copper oxides on superfluid density. Nature 536, 309–311 (2016).
• Yu, Y. et al. High-temperature superconductivity in monolayer Bi₂Sr₂CaCu₂O_8+δ. Nature 575, 156-163 (2019). [XH. Chen/YB. Zhang]

Iron-based superconductors

• Chu, J.-H. et al. In-Plane Resistivity Anisotropy in an Underdoped Iron Arsenide Superconductor. Science 329, 824–826 (2010). [IR. Fisher]
• Kuo, H.-H., Chu, J.-H., Palmstrom, J. C., Kivelson, S. A. & Fisher, I. R. Ubiquitous signatures of nematic quantum criticality in optimally doped Fe-based superconductors. Science 352, 958–962 (2016).

FeSe

• Sprau, P. O. et al. Discovery of orbital-selective Cooper pairing in FeSe. Science 357, 75–80 (2017). [JCS. Davis]

FeSe/STO

• Lee, J. J. et al. Interfacial mode coupling as the origin of the enhancement of T_c in FeSe films on SrTiO₃. Nature 515, 245–248 (2014). [ZX. Shen]

Nickelates

• Li, D. et al. Superconductivity in an infinite-layer nickelate. Nature 572, 624–627 (2019). [HY. Hwang]
• Hepting, M. et al. Electronic structure of the parent compound of superconducting infinite-layer nickelates. Nat. Mater. 19, 381–385 (2020). [WS. Lee]
• Sakakibara, H. et al. Model Construction and a Possibility of Cupratelike Pairing in a New d⁹ Nickelate Superconductor (Nd, Sr)NiO₂. Phys. Rev. Lett. 125, 077003 (2020). [K. Kuroki]
• Wu, X. et al. Robust d_x²-y²-wave superconductivity of infinite-layer nickelates. Phys. Rev. B 101, 060504 (2020). [S. Raghu/R. Thomale]

Sr₂IrO₄

• Kim, Y. K., Sung, N. H., Denlinger, J. D. & Kim, B. J. Observation of a d-wave gap in electron-doped Sr₂IrO₄. Nat. Phys. 12, 37–41 (2015).

Sr₂RuO₄

• Ishida, K. et al. Spin-triplet superconductivity in Sr₂RuO₄ identified by ¹⁷O Knight shift. Nature 396, 658–660 (1998). [Y. Maeno]
• Pustogow, A. et al. Constraints on the superconducting order parameter in Sr₂RuO₄ from oxygen-17 nuclear magnetic resonance. Nature 574, 72-75 (2019). [SE. Brown]
• Ghosh, S. et al. Thermodynamic evidence for a two-component superconducting order parameter in Sr₂RuO₄. Nat. Phys. 17, 199–204 (2020). [BJ. Ramshaw]
• Grinenko, V. et al. Split superconducting and time-reversal symmetry-breaking transitions in Sr₂RuO₄ under stress. Nat. Phys. 17, 748–754 (2021). [CW. Hicks/HH. Klauss]

Cu_xBi₂Se₃

• Matano, K., Kriener, M., Segawa, K., Ando, Y. & Zheng, G. Spin-rotation symmetry breaking in the superconducting state of Cu_xBi₂Se₃. Nat. Phys. 12, 852–854 (2016).
• Yonezawa, S. et al. Thermodynamic evidence for nematic superconductivity in Cu_xBi₂Se₃. Nat. Phys. 13, 123–126 (2016). [Y. Maeno]

Cu_xTiSe₂

• Morosan, E. et al. Superconductivity in Cu_xTiSe₂. Nat. Phys. 2, 544–550 (2006). [RJ. Cava]

Hydrides

• Drozdov, A. P., Eremets, M. I., Troyan, I. A., Ksenofontov, V. & Shylin, S. I. Conventional superconductivity at 203 kelvin at high pressures in the sulfur hydride system. Nature 525, 73–76 (2015).
• Errea, I. et al. Quantum crystal structure in the 250-kelvin superconducting lanthanum hydride. Nature 578, 66–69 (2020). [JA. Flores-Livas]

Higgs modes

• Matsunaga, R. et al. Light-induced collective pseudospin precession resonating with Higgs mode in a superconductor. Science 345, 1145–1149 (2014). [R. Shimano]

Kondo insulators
SmB₆

• Kim, D. J., Xia, J. & Fisk, Z. Topological surface state in the Kondo insulator samarium hexaboride. Nat. Mater. 13, 466–470 (2014).

Mott insulators
1T-TaS₂

• Sipos, B. et al. From Mott state to superconductivity in 1T-TaS₂. Nat. Mater. 7, 960–965 (2008). [E. Tutiš]
• Law, K. T. & Lee, P. A. 1T-TaS₂ as a quantum spin liquid. PNAS 114, 6996–7000 (2017).
• Vaňo, V. et al. Artificial heavy fermions in a van der Waals heterostructure. Nature 599, 582–586 (2021). [P. Liljeroth]

1T-TaSe₂

• Chen, Y. et al. Strong correlations and orbital texture in single-layer 1T-TaSe₂. Nat. Phys. 16, 218–224 (2020). [MF. Crommie]

Photons

• Ma, R. et al. A dissipatively stabilized Mott insulator of photons. Nature 566, 51–57 (2019). [DI. Schuster]

Synthesis

• Li, J. et al. General synthesis of two-dimensional van der Waals heterostructure arrays. Nature 579, 368–374 (2020). [XD. Duan/XF. Duan]

Graphene

• Zhang, Y., Tan, Y.-W., Stormer, H. L. & Kim, P. Experimental observation of the quantum Hall effect and Berry's phase in graphene. Nature 438, 201–204 (2005).
• Wunsch, B., Stauber, T., Sols, F. & Guinea, F. Dynamical polarization of graphene at finite doping. New J. Phys. 8, 318–318 (2006).
• Cheianov, V. V., Fal’ko, V. & Altshuler, B. L. The Focusing of Electron Flow and a Veselago Lens in Graphene p-n Junctions. Science 315, 1252–1255 (2007).
• Xiao, D., Yao, W. & Niu, Q. Valley-Contrasting Physics in Graphene: Magnetic Moment and Topological Transport. Phys. Rev. Lett. 99, 236809 (2007).
• Novoselov, K. S. et al. Room-Temperature Quantum Hall Effect in Graphene. Science 315, 1379–1379 (2007). [P. Kim/AK. Geim]
• Balandin, A. A. et al. Superior Thermal Conductivity of Single-Layer Graphene. Nano Lett. 8, 902–907 (2008). [CN. Lau]
• Ghosh, S. et al. Extremely high thermal conductivity of graphene: Prospects for thermal management applications in nanoelectronic circuits. Appl. Phys. Lett. 92, 151911 (2008).
• Seol, J. H. et al. Two-Dimensional Phonon Transport in Supported Graphene. Science 328, 213–216 (2010). [L. Shi]
• Crassee, I. et al. Giant Faraday rotation in single- and multilayer graphene. Nat. Phys. 7, 48–51 (2011). [AB. Kuzmenko]
• Gorbachev, R. V. et al. Detecting topological currents in graphene superlattices. Science 346, 448–451 (2014). [LS. Levitov/AK. Geim]
• Chen, S. et al. Electron optics with p-n junctions in ballistic graphene. Science 353, 1522–1525 (2016). [CR. Dean]
• Luong, D. X. et al. Gram-scale bottom-up flash graphene synthesis. Nature 577, 647–651 (2020). [R. Shahsavari/BI. Yakobson/JM. Tour]
• Ku, M. J. H. et al. Imaging viscous flow of the Dirac fluid in graphene. Nature 583, 537–541 (2020). [A. Yacoby/RL. Walsworth]
• McIver, J. W. et al. Light-induced anomalous Hall effect in graphene. Nat. Phys. 16, 38-41 (2020). [A. Cavalleri]
• Wang, L., Sofer, Z. & Pumera, M. Will Any Crap We Put into Graphene Increase Its Electrocatalytic Effect? ACS Nano 14, 21–25 (2020).

Bernal-stacked bilayer graphene

• de la Barrera, S. C. et al. Cascade of isospin phase transitions in Bernal-stacked bilayer graphene at zero magnetic field. Nat. Phys. 18, 771–775 (2022). [P. Jarillo-Herrero/R. Ashoori]

Transition metal dichalcogenides (TMD)
XY₂ (X = Mo, W; Y = S, Se)

• Kozawa, D. et al. Photocarrier relaxation pathway in two-dimensional semiconducting transition metal dichalcogenides. Nat. Commun. 5, 4543 (2014). [G. Eda]

XTe₂ (X = Mo, W)

• Wang, Z., Wieder, B. J., Li, J., Yan, B. & Bernevig, B. A. Higher-Order Topology, Monopole Nodal Lines, and the Origin of Large Fermi Arcs in Transition Metal Dichalcogenides XTe₂ (X = Mo, W). Phys. Rev. Lett. 123, 186401 (2019).

MoS₂

• Yan, R. et al. Thermal Conductivity of Monolayer Molybdenum Disulfide Obtained from Temperature-Dependent Raman Spectroscopy. ACS Nano 8, 986–993 (2013). [ARH. Walker/HG. Xing]
• Zhang, X. et al. Measurement of Lateral and Interfacial Thermal Conductivity of Single- and Bilayer MoS₂ and MoSe₂ Using Refined Optothermal Raman Technique. ACS Appl. Mater. Interfaces 7, 25923–25929 (2015). [JC. Hone]
• Wang, H. et al. Integrated Circuits Based on Bilayer MoS₂ Transistors. Nano Lett. 12, 4674–4680 (2012). [T. Palacios]
• Mak, K. F., McGill, K. L., Park, J. & McEuen, P. L. The valley Hall effect in MoS₂ transistors. Science 344, 1489–1492 (2014).
• Liu, X. et al. Strong light–matter coupling in two-dimensional atomic crystals. Nat. Photon. 9, 30–34 (2014). [VM. Menon]
• Sarkar, D. et al. A subthermionic tunnel field-effect transistor with an atomically thin channel. Nature 526, 91–95 (2015). [K. Banerjee]
• Lu, J. M. et al. Evidence for two-dimensional Ising superconductivity in gated MoS₂. Science 350, 1353–1357 (2015). [JT. Ye]
• Kim, S. E. et al. Extremely anisotropic van der Waals thermal conductors. Nature 597, 660–665 (2021). [P. Erhart/DG. Cahill/JW. Park]

MoSe₂/hBN/MoSe₂

• Zhou, Y. et al. Bilayer Wigner crystals in a transition metal dichalcogenide heterostructure. Nature 595, 48–52 (2021). [E. Demler/HK. Park]

WS₂

• Zhang, Y. J. et al. Enhanced intrinsic photovoltaic effect in tungsten disulfide nanotubes. Nature 570, 349–353 (2019). [Y. Iwasa]
• Benítez, L. A. et al. Tunable room-temperature spin galvanic and spin Hall effects in van der Waals heterostructures. Nat. Mater. 19, 170–175 (2020). [SO. Valenzuela]

WSe₂

• Chiritescu, C. et al. Ultralow Thermal Conductivity in Disordered, Layered WSe₂ Crystals. Science 315, 351–353 (2007). [DG. Cahill/P. Zschack]
• Zhu, H. et al. Observation of chiral phonons. Science 359, 579–582 (2018). [Y. Wang/X. Zhang]

WTe₂

• Wang, Y. et al. Gate-tunable negative longitudinal magnetoresistance in the predicted type-II Weyl semimetal WTe₂. Nat. Commun. 7, 13142 (2016). [BG. Wang/XG. Wan/F. Miao]
• Ma, Q. et al. Observation of the nonlinear Hall effect under time-reversal-symmetric conditions. Nature 565, 337-342 (2018). [N. Gedik/P. Jarillo-Herrero]
• Wu, S. et al. Observation of the quantum spin Hall effect up to 100 kelvin in a monolayer crystal. Science 359, 76-79 (2018). [P. Jarillo-Herrero]
• Sie, E. J. et al. An ultrafast symmetry switch in a Weyl semimetal. Nature 565, 61-66 (2019). [AM. Lindenberg]

NiI₂

• Song, Q. et al. Evidence for a single-layer van der Waals multiferroic. Nature 602, 601–605 (2022). [R. Comin]

Contacts for semiconductors

• Shen, P.-C. et al. Ultralow contact resistance between semimetal and monolayer semiconductors. Nature 593, 211–217 (2021). [LJ. Li/J. Kong]
• Wang, Y. et al. P-type electrical contacts for 2D transition-metal dichalcogenides. Nature 610, 61–66 (2022). [M. Chhowalla]

Two-dimensional FM/AFM
CrX₃ (X = Cl, Br, I)

• Chen, W. et al. Direct observation of van der Waals stacking–dependent interlayer magnetism. Science 366, 983–987 (2019). [SW. Wu/CL. Gao]

CrCl₃

• Klein, D. R. et al. Enhancement of interlayer exchange in an ultrathin two-dimensional magnet. Nat. Phys. 15, 1255-1260 (2019). [P. Jarillo-Herrero]

CrI₃

• Huang, B. et al. Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit. Nature 546, 270–273 (2017). [P. Jarillo-Herrero/XD. Xu]
• Klein, D. R. et al. Probing magnetism in 2D van der Waals crystalline insulators via electron tunneling. Science 360, 1218–1222 (2018). [P. Jarillo-Herrero]
• Seyler, K. L. et al. Ligand-field helical luminescence in a 2D ferromagnetic insulator. Nat. Phys. 14, 277–281 (2018). [P. Jarillo-Herrero/XD. Xu]
• Huang, B. et al. Electrical control of 2D magnetism in bilayer CrI₃. Nat. Nanotechnol. 13, 544–548 (2018). [P. Jarillo-Herrero/XD. Xu]
• Chen, L. et al. Topological Spin Excitations in Honeycomb Ferromagnet CrI₃. Phys. Rev. X 8, 041028 (2018). [PC. Dai]
• Song, T. et al. Switching 2D magnetic states via pressure tuning of layer stacking. Nat. Mater. 18, 1298-1302 (2019). [XD. Xu]
• Li, T. et al. Pressure-controlled interlayer magnetism in atomically thin CrI₃. Nat. Mater. 18, 1303-1308 (2019). [KF. Mak/J. Shan]
• Lee, I. et al. Fundamental Spin Interactions Underlying the Magnetic Anisotropy in the Kitaev Ferromagnet CrI₃. Phys. Rev. Lett. 124, 017201 (2020). [PC. Hammel]
• Cenker, J. et al. Direct observation of two-dimensional magnons in atomically thin CrI₃. Nat. Phys. 17, 20–25 (2021). [D. Xiao/XD. Xu]

CrI₃/WSe₂

• Zhong, D. et al. Layer-resolved magnetic proximity effect in van der Waals heterostructures. Nat. Nanotechnol. 15, 187–191 (2020). [XD. Xu]

Fe₃GeTe₂

• Kim, K. et al. Large anomalous Hall current induced by topological nodal lines in a ferromagnetic van der Waals semimetal. Nat. Mater. 17, 794–799 (2018). [BJ. Yang/JS. Kim]
• Tan, C. et al. Hard magnetic properties in nanoflake van der Waals Fe₃GeTe₂. Nat. Commun. 9, 1554 (2018). [L. Wang/CG. Lee]
• Wang, X. et al. Current-driven magnetization switching in a van der Waals ferromagnet Fe₃GeTe₂. Sci. Adv. 5, eaaw8904 (2019). [Z. Han/GY. Zhang/GQ. Yu/XF. Han]

Fe₄GeTe₂

• Seo, J. et al. Nearly room temperature ferromagnetism in a magnetic metal-rich van der Waals metal. Sci. Adv. 6, eaay8912 (2020). [SY. Choi/JH. Shim/JS. Kim]

MnBi₂Te₄

• Otrokov, M. M. et al. Prediction and observation of an antiferromagnetic topological insulator. Nature 576, 416–422 (2019). [EV. Chulkov]
• Hao, Y.-J. et al. Gapless Surface Dirac Cone in Antiferromagnetic Topological Insulator MnBi₂Te₄. Phys. Rev. X 9, 041038 (2019). [CY. Chen/QH. Liu/C. Liu]
• Chen, Y. J. et al. Topological Electronic Structure and Its Temperature Evolution in Antiferromagnetic Topological Insulator MnBi₂Te₄. Phys. Rev. X 9, 041040 (2019). [ZK. Liu/LX. Yang/YL. Chen]
• Deng, Y. et al. Quantum anomalous Hall effect in intrinsic magnetic topological insulator MnBi₂Te₄. Science 367, 895-900 (2020). [J. Wang/XH. Chen/YB. Zhang]
• Liu, C. et al. Robust axion insulator and Chern insulator phases in a two-dimensional antiferromagnetic topological insulator. Nat. Mater. 19, 522-527 (2020). [Y. Xu/JS. Zhang/YY. Wang]
• Swatek, P. et al. Gapless Dirac surface states in the antiferromagnetic topological insulator MnBi₂Te₄. Phys. Rev. B 101, 161109 (2020). [A. Kaminski]
• Gao, A. et al. Layer Hall effect in a 2D topological axion antiferromagnet. Nature 595, 521–525 (2021). [N. Ni/SY. Xu]

MnBi₄Te₇

• Hu, C. et al. A van der Waals antiferromagnetic topological insulator with weak interlayer magnetic coupling. Nat. Commun. 11, 97 (2020). [QH. Liu/D. Dessau/N. Ni]

MnBi_2nTe_3n+1

• Li, H. et al. Dirac Surface States in Intrinsic Magnetic Topological Insulators EuSn₂As₂ and MnBi_2nTe_3n+1. Phys. Rev. X 9, 041039 (2019). [WT. Zhang/HM. Weng/T. Qian/H. Ding]
• Zhang, R.-X., Wu, F. & Das Sarma, S. Möbius Insulator and Higher-Order Topology in MnBi_2nTe_3n+1. Phys. Rev. Lett. 124, 136407 (2020).

MnBi_2-xSb_xTe₄

• Yan, J.-Q. et al. Evolution of structural, magnetic, and transport properties in MnBi_2-xSb_xTe₄. Phys. Rev. B 100, 104409 (2019). [BC. Sales]

EnSn₂As₂

• Li, H. et al. Dirac Surface States in Intrinsic Magnetic Topological Insulators EuSn₂As₂ and MnBi_2nTe_3n+1. Phys. Rev. X 9, 041039 (2019). [WT. Zhang/HM. Weng/T. Qian/H. Ding]

III-V semiconductors
hBN

• Ma, K. Y. et al. Epitaxial single-crystal hexagonal boron nitride multilayers on Ni(111). Nature 606, 88–93 (2022). [RS. Ruoff/M. Chhowalla/F. Ding/HS. Shin]

InP

• Kim, Y. et al. Remote epitaxy through graphene enables two-dimensional material-based layer transfer. Nature 544, 340–343 (2017). [JH. Kim]

GaN

• Chung, K., Lee, C.-H. & Yi, G.-C. Transferable GaN Layers Grown on ZnO-Coated Graphene Layers for Optoelectronic Devices. Science 330, 655–657 (2010).
• Kim, J. et al. Principle of direct van der Waals epitaxy of single-crystalline films on epitaxial graphene. Nat. Commun. 5, 4836 (2014). [DK. Sadana]

GaP

• Kim, Y. et al. Remote epitaxy through graphene enables two-dimensional material-based layer transfer. Nature 544, 340–343 (2017). [JH. Kim]

GaAs

• Kim, Y. et al. Remote epitaxy through graphene enables two-dimensional material-based layer transfer. Nature 544, 340–343 (2017). [JH. Kim]

Heterostructures/Superlattices
Theory

• Esaki, L. & Tsu, R. Superlattice and Negative Differential Conductivity in Semiconductors. IBM J. Res. Dev. 14, 61–65 (1970).
• Chen, G. Thermal conductivity and ballistic-phonon transport in the cross-plane direction of superlattices. Phys. Rev. B 57, 14958–14973 (1998).

Heterostructures of (Bi,Sb)₂Te₃

• Xiao, D. et al. Realization of the Axion Insulator State in Quantum Anomalous Hall Sandwich Heterostructures. Phys. Rev. Lett. 120, 056801 (2018). [N. Samarth/CZ. Chang]

EuS/Bi₂Se₃

• Katmis, F. et al. A high-temperature ferromagnetic topological insulating phase by proximity coupling. Nature 533, 513–516 (2016). [JS. Moodera]

EuS/graphene

• Wei, P. et al. Strong interfacial exchange field in the graphene/EuS heterostructure. Nat. Mater. 15, 711–716 (2016). [CT. Chen]

SrTiO₃/PbTiO₃

• Yadav, A. K. et al. Observation of polar vortices in oxide superlattices. Nature 530, 198–201 (2016). [R. Ramesh]
• Yadav, A. K. et al. Spatially resolved steady-state negative capacitance. Nature 565, 468–471 (2019). [S. Salahuddin]

Bi₂Te₃/MnBi₂Te₄

• Rienks, E. D. L. et al. Large magnetic gap at the Dirac point in Bi₂Te₃/MnBi₂Te₄ heterostructures. Nature 576, 423–428 (2019). [O. Rader/G. Springholz]

GaAs/AlGaAs

• Tsui, D. C., Stormer, H. L. & Gossard, A. C. Two-Dimensional Magnetotransport in the Extreme Quantum Limit. Phys. Rev. Lett. 48, 1559–1562 (1982).
• Willett, R. et al. Observation of an even-denominator quantum number in the fractional quantum Hall effect. Phys. Rev. Lett. 59, 1776–1779 (1987). [JH. English]
• de-Picciotto, R. et al. Direct observation of a fractional charge. Nature 389, 162–164 (1997). [D. Mahalu]
• Banerjee, M. et al. Observation of half-integer thermal Hall conductance. Nature 559, 205-210 (2018). [A. Stern]

Moiré heterostructures
Twisted bilayer graphene

• Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018). [P. Jarillo-Herrero]
• Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018). [P. Jarillo-Herrero]
• Kerelsky, A. et al. Maximized electron interactions at the magic angle in twisted bilayer graphene. Nature 572, 95-100 (2019). [A. Rubio/AN. Pasupathy]
• Xie, Y. et al. Spectroscopic signatures of many-body correlations in magic-angle twisted bilayer graphene. Nature 572, 101-105 (2019). [A. Yazdani]
• Jiang, Y. et al. Charge order and broken rotational symmetry in magic-angle twisted bilayer graphene. Nature 573, 91–95 (2019). [JH. Mao/EY. Andrei]
• Lu, X. et al. Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene. Nature 574, 653–657 (2019). [DK. Efetov]
• Sharpe, A. L. et al. Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene. Science 365, 605–608 (2019). [D. Goldhaber-Gordon]
• Polshyn, H. et al. Large linear-in-temperature resistivity in twisted bilayer graphene. Nat. Phys. 15, 1011-1016 (2019). [CR. Dean/AF. Young]
• Choi, Y. et al. Electronic correlations in twisted bilayer graphene near the magic angle. Nat. Phys. 15, 1174-1180 (2019). [S. Nadj-Perge]
• Park, M. J., Kim, Y., Cho, G. Y. & Lee, S. Higher-Order Topological Insulator in Twisted Bilayer Graphene. Phys. Rev. Lett. 123, 216803 (2019).
• Zhang, Y.-H., Mao, D. & Senthil, T. Twisted bilayer graphene aligned with hexagonal boron nitride: Anomalous Hall effect and a lattice model. Phys. Rev. Research 1, 033126 (2019).
• Wong, D. et al. Cascade of electronic transitions in magic-angle twisted bilayer graphene. Nature 582, 198–202 (2020). [A. Yazdani]
• Zondiner, U. et al. Cascade of phase transitions and Dirac revivals in magic-angle graphene. Nature 582, 203–208 (2020). [P. Jarillo-Herrero/S. Ilani]
• Arora, H. S. et al. Superconductivity in metallic twisted bilayer graphene stabilized by WSe₂. Nature 583, 379–384 (2020). [S. Nadj-Perge]
• Nuckolls, K. P. et al. Strongly correlated Chern insulators in magic-angle twisted bilayer graphene. Nature 588, 610–615 (2020). [A. Yazdani]
• Serlin, M. et al. Intrinsic quantized anomalous Hall effect in a moiré heterostructure. Science 367, 900-903 (2020). [AF. Young]
• Saito, Y., Ge, J., Watanabe, K., Taniguchi, T. & Young, A. F. Independent superconductors and correlated insulators in twisted bilayer graphene. Nat. Phys. 16, 926–930 (2020). [AF. Young]
• Lisi, S. et al. Observation of flat bands in twisted bilayer graphene. Nat. Phys. 17, 189–193 (2020). [F. Baumberger]
• Xie, M. & MacDonald, A. H. Nature of the Correlated Insulator States in Twisted Bilayer Graphene. Phys. Rev. Lett. 124, 097601 (2020).
• Cao, Y. et al. Strange Metal in Magic-Angle Graphene with near Planckian Dissipation. Phys. Rev. Lett. 124, 076801 (2020). [T. Senthil/P. Jarillo-Herrero]
• Julku, A., Peltonen, T. J., Liang, L., Heikkilä, T. T. & Törmä, P. Superfluid weight and Berezinskii-Kosterlitz-Thouless transition temperature of twisted bilayer graphene. Phys. Rev. B 101, 060505 (2020).
• Cea, T. & Guinea, F. Band structure and insulating states driven by Coulomb interaction in twisted bilayer graphene. Phys. Rev. B 102, 045107 (2020).
• Ledwith, P. J., Tarnopolsky, G., Khalaf, E. & Vishwanath, A. Fractional Chern insulator states in twisted bilayer graphene: An analytical approach. Phys. Rev. Research 2, 023237 (2020).
• Gadelha, A. C. et al. Localization of lattice dynamics in low-angle twisted bilayer graphene. Nature 590, 405–409 (2021). [A. Jorio]
• Cao, Y. et al. Nematicity and competing orders in superconducting magic-angle graphene. Science 372, 264–271 (2021). [P. Jarillo-Herrero]
• Das, I. et al. Symmetry-broken Chern insulators and Rashba-like Landau-level crossings in magic-angle bilayer graphene. Nat. Phys. 17, 710–714 (2021). [DK. Efetov]
• Khalaf, E., Chatterjee, S., Bultinck, N., Zaletel, M. P. & Vishwanath, A. Charged skyrmions and topological origin of superconductivity in magic-angle graphene. Sci. Adv. 7, eabf5299 (2021).
• Jaoui, A. et al. Quantum critical behaviour in magic-angle twisted bilayer graphene. Nat. Phys. 18, 633–638 (2022). [DK. Efetov]
• Grover, S. et al. Chern mosaic and Berry-curvature magnetism in magic-angle graphene. Nat. Phys. 18, 885–892 (2022).

Twisted double bilayer graphene

• Burg, G. W. et al. Correlated Insulating States in Twisted Double Bilayer Graphene. Phys. Rev. Lett. 123, 197702 (2019). [E. Tutuc]
• Cao, Y. et al. Tunable correlated states and spin-polarized phases in twisted bilayer–bilayer graphene. Nature 583, 215-220 (2020). [P. Jarillo-Herrero]
• Shen, C. et al. Correlated states in twisted double bilayer graphene. Nat. Phys. 16, 520–525 (2020). [GY. Zhang]

ABC-trilayer graphene on h-BN

• Chen, G. et al. Signatures of tunable superconductivity in a trilayer graphene moiré superlattice. Nature 572, 215–219 (2019). [D. Goldhaber-Gordon/YB. Zhang/F. Wang]
• Chen, G. et al. Tunable correlated Chern insulator and ferromagnetism in a moiré superlattice. Nature 579, 56–61 (2020). [D. Goldhaber-Gordon/YB. Zhang/F. Wang]

Twisted trilayer graphene

• Park, J. M., Cao, Y., Watanabe, K., Taniguchi, T. & Jarillo-Herrero, P. Tunable strongly coupled superconductivity in magic-angle twisted trilayer graphene. Nature 590, 249–255 (2021).
• Kim, H. et al. Evidence for unconventional superconductivity in twisted trilayer graphene. Nature 606, 494–500 (2022). [S. Nadj-Perge]
• Lin, J.-X. et al. Zero-field superconducting diode effect in small-twist-angle trilayer graphene. Nat. Phys. 18, 1221–1227 (2022). [JIA. Li]

MoTe₂/WSe₂

• Li, T. et al. Quantum anomalous Hall effect from intertwined moiré bands. Nature 600, 641–646 (2021). [J. Shan/KF. Mak]

WSe₂/WSe₂

• Xu, Y. et al. A tunable bilayer Hubbard model in twisted WSe₂. Nat. Nanotechnol. 17, 934–939 (2022). [KF. Mak/J. Shan]

WSe₂/WS₂

• Tang, Y. et al. Simulation of Hubbard model physics in WSe₂/WS₂ moiré superlattices. Nature 579, 353–358 (2020). [J. Shan/KF. Mak]
• Regan, E. C. et al. Mott and generalized Wigner crystal states in WSe₂/WS₂ moiré superlattices. Nature 579, 359–363 (2020). [F. Wang]

Excitons

• Elliott, R. J. Intensity of Optical Absorption by Excitons. Phys. Rev. 108, 1384–1389 (1957).
• Fogler, M. M., Butov, L. V. & Novoselov, K. S. High-temperature superfluidity with indirect excitons in van der Waals heterostructures. Nat. Commun. 5, 4555 (2014).
• You, Y. et al. Observation of biexcitons in monolayer WSe₂. Nat. Phys. 11, 477–481 (2015). [TF. Heinz]
• Kogar, A. et al. Signatures of exciton condensation in a transition metal dichalcogenide. Science 358, 1314–1317 (2017). [P. Abbamonte]
• Zhou, Y. et al. Probing dark excitons in atomically thin semiconductors via near-field coupling to surface plasmon polaritons. Nat. Nanotechnol. 12, 856–860 (2017). [P. Kim/MD. Lukin/HK. Park]
• Jauregui, L. A. et al. Electrical control of interlayer exciton dynamics in atomically thin heterostructures. Science 366, 870–875 (2019). [P. Kim]
• Shimazaki, Y. et al. Strongly correlated electrons and hybrid excitons in a moiré heterostructure. Nature 580, 472–477 (2020). [A. Imamoğlu]
• Madéo, J. et al. Directly visualizing the momentum-forbidden dark excitons and their dynamics in atomically thin semiconductors. Science 370, 1199–1204 (2020). [KM. Dani]
• Bai, Y. et al. Excitons in strain-induced one-dimensional moiré potentials at transition metal dichalcogenide heterojunctions. Nat. Mater. 19, 1068–1073 (2020). [AN. Pasupathy/XY. Zhu]
• He, M. et al. Valley phonons and exciton complexes in a monolayer semiconductor. Nat. Commun. 11, 618 (2020). [H. Dery/W. Yao/XD. Xu]
• Ma, L. et al. Strongly correlated excitonic insulator in atomic double layers. Nature 598, 585–589 (2021). [KF. Mak/J. Shan]

Oxides/Perovskites
BaTiO₃

• Kum, H. S. et al. Heterogeneous integration of single-crystalline complex-oxide membranes. Nature 578, 75–81 (2020). [JH. Kim]

BiFeO₃

• Ji, D. et al. Freestanding crystalline oxide perovskites down to the monolayer limit. Nature 570, 87–90 (2019). [P. Wang/YF. Nie/XQ. Pan]

CoFe₂O₄

• Kum, H. S. et al. Heterogeneous integration of single-crystalline complex-oxide membranes. Nature 578, 75–81 (2020). [JH. Kim]

DyFeO₃

• Kimel, A. V. et al. Ultrafast non-thermal control of magnetization by instantaneous photomagnetic pulses. Nature 435, 655–657 (2005). [T. Rasing]

La_0.7Ca_0.3MnO₃

• Hong, S. S. et al. Extreme tensile strain states in La_0.7Ca_0.3MnO₃ membranes. Science 368, 71–76 (2020). [HY. Hwang]

Pb(Mg_1/3Nb_2/3)O₃–PbTiO₃

• Kum, H. S. et al. Heterogeneous integration of single-crystalline complex-oxide membranes. Nature 578, 75–81 (2020). [JH. Kim]

SrTiO₃

• Ji, D. et al. Freestanding crystalline oxide perovskites down to the monolayer limit. Nature 570, 87–90 (2019). [P. Wang/YF. Nie/XQ. Pan]
• Kum, H. S. et al. Heterogeneous integration of single-crystalline complex-oxide membranes. Nature 578, 75–81 (2020). [JH. Kim]

Y₃Fe₅O₁₂ (YIG)

• Kum, H. S. et al. Heterogeneous integration of single-crystalline complex-oxide membranes. Nature 578, 75–81 (2020). [JH. Kim]

Hybrid perovskites

• Wang, J. et al. Templated growth of oriented layered hybrid perovskites on 3D-like perovskites. Nat. Commun. 11, 582 (2020). [JS. Huang/YB. Yuan]

VO₂

• Lee, D. et al. Isostructural metal-insulator transition in VO₂. Science 362, 1037–1040 (2018). [CB. Eom]

Others
Ni₈₀Fe₂₀

• Nembach, H. T., Shaw, J. M., Weiler, M., Jué, E. & Silva, T. J. Linear relation between Heisenberg exchange and interfacial Dzyaloshinskii–Moriya interaction in metal films. Nat. Phys. 11, 825–829 (2015).

NbOCl₂

• Guo, Q. et al. Ultrathin quantum light source with van der Waals NbOCl₂ crystal. Nature 613, 53–59 (2023). [XF. Ren/CW. Qiu/SJ. Pennycook/ATS. Wee]

Carbon-based compounds

• Mounet, N. & Marzari, N. First-principles determination of the structural, vibrational and thermodynamic properties of diamond, graphite, and derivatives. Phys. Rev. B 71, 205214 (2005).

Graphite

• Piscanec, S., Lazzeri, M., Mauri, F., Ferrari, A. C. & Robertson, J. Kohn Anomalies and Electron-Phonon Interactions in Graphite. Phys. Rev. Lett. 93, 185503 (2004).
• Huberman, S. et al. Observation of second sound in graphite at temperatures above 100 K. Science 364, 375–379 (2019). [G. Chen/KA. Nelson]

Graphene nanoribbons

• Rizzo, D. J. et al. Topological band engineering of graphene nanoribbons. Nature 560, 204–208 (2018). [SG. Louie/MF. Crommie/FR. Fischer]
• Gröning, O. et al. Engineering of robust topological quantum phases in graphene nanoribbons. Nature 560, 209–213 (2018). [R. Fasel]

Carbon nanotubes

• Bockrath, M. et al. Luttinger-liquid behaviour in carbon nanotubes. Nature 397, 598–601 (1999). [PL. McEuen]
• Berber, S., Kwon, Y.-K. & Tománek, D. Unusually High Thermal Conductivity of Carbon Nanotubes. Phys. Rev. Lett. 84, 4613–4616 (2000).
• Kim, P., Shi, L., Majumdar, A. & McEuen, P. L. Thermal Transport Measurements of Individual Multiwalled Nanotubes. Phys. Rev. Lett. 87, 215502 (2001).
• Shi, L. et al. Measuring Thermal and Thermoelectric Properties of One-Dimensional Nanostructures Using a Microfabricated Device. J. Heat Transfer 125, 881–888 (2003).
• Kuemmeth, F., Ilani, S., Ralph, D. C. & McEuen, P. L. Coupling of spin and orbital motion of electrons in carbon nanotubes. Nature 452, 448–452 (2008).
• Xiang, R. et al. One-dimensional van der Waals heterostructures. Science 367, 537–542 (2020). [S. Maruyama]

Charge density wave

• Kogar, A. et al. Light-induced charge density wave in LaTe₃. Nat. Phys. 16, 159-163 (2020). [N. Gedik]

Other group-IV materials (Si, Ge)

• Fadaly, E. M. T. et al. Direct-bandgap emission from hexagonal Ge and SiGe alloys. Nature 580, 205–209 (2020). [EPAM. Bakkers]

Majoranas
Semiconducting nanowires

• Mourik, V. et al. Signatures of Majorana Fermions in Hybrid Superconductor-Semiconductor Nanowire Devices. Science 336, 1003–1007 (2012). [LP. Kouwenhoven]
• Rokhinson, L. P., Liu, X. & Furdyna, J. K. The fractional a.c. Josephson effect in a semiconductor–superconductor nanowire as a signature of Majorana particles. Nat. Phys. 8, 795–799 (2012).
• Albrecht, S. M. et al. Exponential protection of zero modes in Majorana islands. Nature 531, 206–209 (2016). [CM. Marcus]
• Vaitiekėnas, S. et al. Flux-induced topological superconductivity in full-shell nanowires. Science 367, eaav3392 (2020). [RM. Lutchyn/CM. Marcus]

Quantum-dot-nanowire hybrid

• Deng, M. T. et al. Majorana bound state in a coupled quantum-dot hybrid-nanowire system. Science 354, 1557–1562 (2016). [CM. Marcus]

Fe chain

• Nadj-Perge, S. et al. Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor. Science 346, 602–607 (2014). [A. Yazdani]
• Jeon, S. et al. Distinguishing a Majorana zero mode using spin-resolved measurements. Science 358, 772–776 (2017). [A. Yazdani]

FeTe_0.55Se_0.45

• Wang, D. et al. Evidence for Majorana bound states in an iron-based superconductor. Science 362, 333–335 (2018). [H. Ding/HJ. Gao]
• Kong, L. et al. Half-integer level shift of vortex bound states in an iron-based superconductor. Nat. Phys. 15, 1181-1187 (2019). [L. Fu/HJ. Gao/H. Ding]
• Zhu, S. et al. Nearly quantized conductance plateau of vortex zero mode in an iron-based superconductor. Science 367, 189–192 (2020). [YY. Zhang/H. Ding/HJ. Gao]

Planar Josephson junctions

• Fornieri, A. et al. Evidence of topological superconductivity in planar Josephson junctions. Nature 569, 89–92 (2019). [CM. Marcus/F. Nichele]
• Ren, H. et al. Topological superconductivity in a phase-controlled Josephson junction. Nature 569, 93–98 (2019). [A. Yacoby]

Quantum dots
Single quantum dots

• Goldhaber-Gordon, D. et al. Kondo effect in a single-electron transistor. Nature 391, 156–159 (1998). [MA. Kastner]
• Cronenwett, S. M., Oosterkamp, T. H. & Kouwenhoven, L. P. A Tunable Kondo Effect in Quantum Dots. Science 281, 540–544 (1998).

Embedded in materials

• Harman, T. C., Taylor, P. J., Walsh, M. P. & LaForge, B. E. Quantum Dot Superlattice Thermoelectric Materials and Devices. Science 297, 2229–2232 (2002).
• Faleev, S. V. & Léonard, F. Theory of enhancement of thermoelectric properties of materials with nanoinclusions. Phys. Rev. B 77, 214304 (2008).
• Ning, Z. et al. Quantum-dot-in-perovskite solids. Nature 523, 324–328 (2015). [EH. Sargent]
• Zhao, W. et al. Superparamagnetic enhancement of thermoelectric performance. Nature 549, 247–251 (2017). [J. Shi]

Alloys

• Han, L. et al. A mechanically strong and ductile soft magnet with extremely low coercivity. Nature 608, 310–316 (2022). [ZM. Li/D. Raabe]

Ferroelectrics

• Shi, Y. et al. A ferroelectric-like structural transition in a metal. Nat. Mater. 12, 1024–1027 (2013). [AT. Boothroyd]
• Ashida, Y. et al. Quantum Electrodynamic Control of Matter: Cavity-Enhanced Ferroelectric Phase Transition. Phys. Rev. X 10, 041027 (2020). [E. Demler]
• Yun, Y. et al. Intrinsic ferroelectricity in Y-doped HfO₂ thin films. Nat. Mater. 21, 903–909 (2022). [EY. Tsymbal/A. Gruverman/XS. Xu]
• Miao, L.-P. et al. Direct observation of geometric and sliding ferroelectricity in an amphidynamic crystal. Nat. Mater. 21, 1158–1164 (2022). [S. Dong/Y. Zhang]

Caloric materials

• Mischenko, A. S., Zhang, Q., Scott, J. F., Whatmore, R. W. & Mathur, N. D. Giant Electrocaloric Effect in Thin-Film PbZr_0.95Ti_0.05O₃. Science 311, 1270–1271 (2006).
• Nair, B. et al. Large electrocaloric effects in oxide multilayer capacitors over a wide temperature range. Nature 575, 468–472 (2019). [X. Moya/S. Hirose/ND. Mathur]
• Torelló, A. et al. Giant temperature span in electrocaloric regenerator. Science 370, 125–129 (2020). [E. Defay]
• Wang, Y. et al. A high-performance solid-state electrocaloric cooling system. Science 370, 129–133 (2020). [D. Schwartz]

Thermoelectrics

• Hicks, L. D. & Dresselhaus, M. S. Effect of quantum-well structures on the thermoelectric figure of merit. Phys. Rev. B 47, 12727–12731 (1993).
• Venkatasubramanian, R., Siivola, E., Colpitts, T. & O’Quinn, B. Thin-film thermoelectric devices with high room-temperature figures of merit. Nature 413, 597–602 (2001).
• Hochbaum, A. I. et al. Enhanced thermoelectric performance of rough silicon nanowires. Nature 451, 163–167 (2008). [A. Majumdar/PD. Yang]
• Boukai, A. I. et al. Silicon nanowires as efficient thermoelectric materials. Nature 451, 168–171 (2008). [JR. Heath]
• Poudel, B. et al. High-Thermoelectric Performance of Nanostructured Bismuth Antimony Telluride Bulk Alloys. Science 320, 634–638 (2008). [G. Chen/ZF. Ren]
• Bubnova, O. et al. Semi-metallic polymers. Nat. Mater. 13, 190–194 (2013). [X. Crispin]
• Zhao, L.-D. et al. Ultrahigh power factor and thermoelectric performance in hole-doped single-crystal SnSe. Science 351, 141–144 (2015). [MG. Kanatzidis]
• Hinterleitner, B. et al. Thermoelectric performance of a metastable thin-film Heusler alloy. Nature 576, 85-90 (2019). [E. Bauer]
• Su, L. et al. High thermoelectric performance realized through manipulating layered phonon-electron decoupling. Science 375, 1385–1389 (2022). [C. Chang/LD. Zhao]

Rectification

• Ando, F. et al. Observation of superconducting diode effect. Nature 584, 373–376 (2020). [T. Ono]
• Wu, H. et al. The field-free Josephson diode in a van der Waals heterostructure. Nature 604, 653–656 (2022). [MN. Ali]
• Lin, J.-X. et al. Zero-field superconducting diode effect in small-twist-angle trilayer graphene. Nat. Phys. 18, 1221–1227 (2022). [JIA. Li]
• Pal, B. et al. Josephson diode effect from Cooper pair momentum in a topological semimetal. Nat. Phys. 18, 1228–1233 (2022).
[SSP. Parkin]
• Narita, H. et al. Field-free superconducting diode effect in noncentrosymmetric superconductor/ferromagnet multilayers. Nat. Nanotechnol. 17, 823–828 (2022). [T. Ono]
• Davydova, M., Prembabu, S. & Fu, L. Universal Josephson diode effect. Sci. Adv. 8, eabo0309 (2022).

Topological photonics

• Onoda, M., Murakami, S. & Nagaosa, N. Hall Effect of Light. Phys. Rev. Lett. 93, 083901 (2004).
• Bliokh, K. Y., Niv, A., Kleiner, V. & Hasman, E. Geometrodynamics of spinning light. Nat. Photon. 2, 748–753 (2008).
• Cheng, X. et al. Robust reconfigurable electromagnetic pathways within a photonic topological insulator. Nat. Mater. 15, 542–548 (2016). [AZ. Genack/AB. Khanikaev]

Hydrodynamics
WP₂

• Gooth, J. et al. Thermal and electrical signatures of a hydrodynamic electron fluid in tungsten diphosphide. Nat. Commun. 9, 4093 (2018). [B. Gottsman]

Graphene

• Crossno, J. et al. Observation of the Dirac fluid and the breakdown of the Wiedemann-Franz law in graphene. Science 351, 1058–1061 (2016). [P. Kim/KC. Fong]

Quasicrystals

• Kraus, Y. E., Lahini, Y., Ringel, Z., Verbin, M. & Zilberberg, O. Topological States and Adiabatic Pumping in Quasicrystals. Phys. Rev. Lett. 109, 106402 (2012).

Excitons

• Kazimierczuk, T., Fröhlich, D., Scheel, S., Stolz, H. & Bayer, M. Giant Rydberg excitons in the copper oxide Cu₂O. Nature 514, 343–347 (2014).
• Su, R. et al. Observation of exciton polariton condensation in a perovskite lattice at room temperature. Nat. Phys. 16, 301–306 (2020). [TCH. Liew/QH. Xiong]

Superconducting qubits (+ resonators)

• Wallraff, A. et al. Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics. Nature 431, 162–167 (2004). [RJ. Schoelkopf]
• Blais, A., Huang, R.-S., Wallraff, A., Girvin, S. M. & Schoelkopf, R. J. Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation. Phys. Rev. A 69, 062320 (2004).
• Schuster, D. I. et al. Resolving photon number states in a superconducting circuit. Nature 445, 515–518 (2007). [RJ. Schoelkopf]
• Fink, J. M. et al. Climbing the Jaynes–Cummings ladder and observing its nonlinearity in a cavity QED system. Nature 454, 315–318 (2008). [A. Wallraff]
• Bylander, J. et al. Noise spectroscopy through dynamical decoupling with a superconducting flux qubit. Nat. Phys. 7, 565–570 (2011). [WD. Oliver]
• Kirchmair, G. et al. Observation of quantum state collapse and revival due to the single-photon Kerr effect. Nature 495, 205–209 (2013). [RJ. Schoelkopf]
• Vlastakis, B. et al. Deterministically Encoding Quantum Information Using 100-Photon Schrödinger Cat States. Science 342, 607–610 (2013). [RJ. Schoelkopf]
• Barends, R. et al. Superconducting quantum circuits at the surface code threshold for fault tolerance. Nature 508, 500–503 (2014). [JM. Martinis]
• Mirrahimi, M. et al. Dynamically protected cat-qubits: a new paradigm for universal quantum computation. New J. Phys. 16, 045014 (2014). [MH. Devoret]
• Ristè, D. et al. Detecting bit-flip errors in a logical qubit using stabilizer measurements. Nat. Commun. 6, 6983 (2015). [L. DiCarlo]
• Chou, K. S. et al. Deterministic teleportation of a quantum gate between two logical qubits. Nature 561, 368–373 (2018). [RJ. Schoelkopf]
• Guillaud, J. & Mirrahimi, M. Repetition Cat Qubits for Fault-Tolerant Quantum Computation. Phys. Rev. X 9, 041053 (2019).
• Grimm, A. et al. Stabilization and operation of a Kerr-cat qubit. Nature 584, 205–209 (2020). [MH. Devoret]
• Campagne-Ibarcq, P. et al. Quantum error correction of a qubit encoded in grid states of an oscillator. Nature 584, 368–372 (2020). [MH. Devoret]
• Lachance-Quirion, D. et al. Entanglement-based single-shot detection of a single magnon with a superconducting qubit. Science 367, 425–428 (2020). [Y. Nakamura]
• Lescanne, R. et al. Exponential suppression of bit-flips in a qubit encoded in an oscillator. Nat. Phys. 16, 509-513 (2020). [Z. Leghtas]
• Puri, S. et al. Bias-preserving gates with stabilized cat qubits. Sci. Adv. 6, eaay5901 (2020). [SM. Girvin]
• Hays, M. et al. Coherent manipulation of an Andreev spin qubit. Science 373, 430–433 (2021). [MH. Devoret]
• Place, A. P. M. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nat. Commun. 12, 1779 (2021). [AA. Houck]
• Stehlik, J. et al. Tunable Coupling Architecture for Fixed-Frequency Transmon Superconducting Qubits. Phys. Rev. Lett. 127, 080505 (2021). [OE. Dial]
• Gyenis, A. et al. Experimental Realization of a Protected Superconducting Circuit Derived from the 0-π Qubit. PRX Quantum 2, 010339 (2021). [AA. Houck]

Diamond color centers

• Childress, L. et al. Coherent Dynamics of Coupled Electron and Nuclear Spin Qubits in Diamond. Science 314, 281–285 (2006). [MD. Lukin]
• Bernien, H. et al. Heralded entanglement between solid-state qubits separated by three metres. Nature 497, 86–90 (2013). [R. Hanson]
• Aslam, N., Waldherr, G., Neumann, P., Jelezko, F. & Wrachtrup, J. Photo-induced ionization dynamics of the nitrogen vacancy defect in diamond investigated by single-shot charge state detection. New J. Phys. 15, 013064 (2013).
• Rose, B. C. et al. Observation of an environmentally insensitive solid-state spin defect in diamond. Science 361, 60–63 (2018). [NP. de Leon]
• Trusheim, M. E. et al. Transform-Limited Photons From a Coherent Tin-Vacancy Spin in Diamond. Phys. Rev. Lett. 124, 023602 (2020). [M. Atatüre/D. Englund]

Silicon qubits

• Kane, B. E. A silicon-based nuclear spin quantum computer. Nature 393, 133–137 (1998).
• He, Y. et al. A two-qubit gate between phosphorus donor electrons in silicon. Nature 571, 371–375 (2019). [MY. Simmons]
• Yang, C. H. et al. Operation of a silicon quantum processor unit cell above one kelvin. Nature 580, 350–354 (2020). [AS. Dzurak]
• Petit, L. et al. Universal quantum logic in hot silicon qubits. Nature 580, 355–359 (2020). [M. Veldhorst]

Neutral atoms

• Jaksch, D. et al. Fast Quantum Gates for Neutral Atoms. Phys. Rev. Lett. 85, 2208–2211 (2000). [MD. Lukin]
• Peyronel, T. et al. Quantum nonlinear optics with single photons enabled by strongly interacting atoms. Nature 488, 57–60 (2012) [MD. Lukin/V. Vuletic]
• Tiecke, T. G. et al. Nanophotonic quantum phase switch with a single atom. Nature 508, 241–244 (2014). [V. Vuletic/MD. Lukin]
• Hosten, O., Engelsen, N. J., Krishnakumar, R. & Kasevich, M. A. Measurement noise 100 times lower than the quantum-projection limit using entangled atoms. Nature 529, 505–508 (2016).
• Omran, A. et al. Generation and manipulation of Schrödinger cat states in Rydberg atom arrays. Science 365, 570–574 (2019). [MD. Lukin]
• Levine, H. et al. Parallel Implementation of High-Fidelity Multiqubit Gates with Neutral Atoms. Phys. Rev. Lett. 123, 170503 (2019). [MD. Lukin]
• Bekenstein, R. et al. Quantum metasurfaces with atom arrays. Nat. Phys. 16, 676–681 (2020). [MD. Lukin]
• Madjarov, I. S. et al. High-fidelity entanglement and detection of alkaline-earth Rydberg atoms. Nat. Phys. 16, 857-861 (2020). [M. Endres]

Molecules

• Bayliss, S. L. et al. Optically addressable molecular spins for quantum information processing. Science 370, 1309–1312 (2020). [DE. Freedman/DD. Awschalom]

Trapped ions

• Cirac, J. I. & Zoller, P. Quantum Computations with Cold Trapped Ions. Phys. Rev. Lett. 74, 4091–4094 (1995).
• Monroe, C., Meekhof, D. M., King, B. E., Itano, W. M. & Wineland, D. J. Demonstration of a Fundamental Quantum Logic Gate. Phys. Rev. Lett. 75, 4714–4717 (1995).
• Leibfried, D. et al. Toward Heisenberg-Limited Spectroscopy with Multiparticle Entangled States. Science 304, 1476–1478 (2004). [DJ. Wineland]
• Schmidt, P. O. et al. Spectroscopy Using Quantum Logic. Science 309, 749–752 (2005). [DJ. Wineland]
• Benhelm, J., Kirchmair, G., Roos, C. F. & Blatt, R. Towards fault-tolerant quantum computing with trapped ions. Nat. Phys. 4, 463–466 (2008).
• Monz, T. et al. 14-Qubit Entanglement: Creation and Coherence. Phys. Rev. Lett. 106, 130506 (2011). [R. Blatt]
• Debnath, S. et al. Demonstration of a small programmable quantum computer with atomic qubits. Nature 536, 63–66 (2016). [C. Monroe]
• Flühmann, C. et al. Encoding a qubit in a trapped-ion mechanical oscillator. Nature 566, 513–517 (2019). [JP. Home]
• Figgatt, C. et al. Parallel entangling operations on a universal ion-trap quantum computer. Nature 572, 368–372 (2019). [C. Monroe]
• Egan, L. et al. Fault-tolerant control of an error-corrected qubit. Nature 598, 281-286 (2021). [C. Monroe]
• Joshi, M. K. et al. Observing emergent hydrodynamics in a long-range quantum magnet. Science 376, 720–724 (2022). [M. Knap/CF. Roos]

NMR

• Cory, D. G., Fahmy, A. F. & Havel, T. F. Ensemble quantum computing by NMR spectroscopy. PNAS 94, 1634–1639 (1997).
• Chuang, I. L., Vandersypen, L. M. K., Zhou, X., Leung, D. W. & Lloyd, S. Experimental realization of a quantum algorithm. Nature 393, 143–146 (1998).
• Chuang, I. L., Gershenfeld, N. & Kubinec, M. Experimental Implementation of Fast Quantum Searching. Phys. Rev. Lett. 80, 3408–3411 (1998).

Cold atoms / Ultracold gases

• Parsons, M. F. et al. Site-resolved measurement of the spin-correlation function in the Fermi-Hubbard model. Science 353, 1253–1256 (2016). [M. Greiner]
• Li, J.-R. et al. A stripe phase with supersolid properties in spin–orbit-coupled Bose–Einstein condensates. Nature 543, 91–94 (2017). [W. Ketterle]
• Mazurenko, A. et al. A cold-atom Fermi–Hubbard antiferromagnet. Nature 545, 462–466 (2017). [M. Greiner]
• Guardado-Sanchez, E. et al. Subdiffusion and Heat Transport in a Tilted Two-Dimensional Fermi-Hubbard System. Phys. Rev. X 10, 011042 (2020). [WS. Bakr]

Quantum dots

• Press, D., Ladd, T. D., Zhang, B. & Yamamoto, Y. Complete quantum control of a single quantum dot spin using ultrafast optical pulses. Nature 456, 218–221 (2008).
• Hofstetter, L., Csonka, S., Nygård, J. & Schönenberger, C. Cooper pair splitter realized in a two-quantum-dot Y-junction. Nature 461, 960–963 (2009).
• Borjans, F., Croot, X. G., Mi, X., Gullans, M. J. & Petta, J. R. Resonant microwave-mediated interactions between distant electron spins. Nature 577, 195–198 (2019).

Photons for quantum information

• Turchette, Q. A., Hood, C. J., Lange, W., Mabuchi, H. & Kimble, H. J. Measurement of Conditional Phase Shifts for Quantum Logic. Phys. Rev. Lett. 75, 4710–4713 (1995).
• Pan, J.-W., Bouwmeester, D., Weinfurter, H. & Zeilinger, A. Experimental Entanglement Swapping: Entangling Photons That Never Interacted. Phys. Rev. Lett. 80, 3891–3894 (1998).
• Knill, E., Laflamme, R. & Milburn, G. J. A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001).
• Duan, L.-M., Lukin, M. D., Cirac, J. I. & Zoller, P. Long-distance quantum communication with atomic ensembles and linear optics. Nature 414, 413–418 (2001).
• Gleyzes, S. et al. Quantum jumps of light recording the birth and death of a photon in a cavity. Nature 446, 297–300 (2007). [M. Brune/S. Haroche]
• Lemos, G. B. et al. Quantum imaging with undetected photons. Nature 512, 409–412 (2014). [A. Zeilinger]
• Zhang, X., Zou, C.-L., Jiang, L. & Tang, H. X. Strongly Coupled Magnons and Cavity Microwave Photons. Phys. Rev. Lett. 113, 156401 (2014).
• Schwartz, I. et al. Deterministic generation of a cluster state of entangled photons. Science 354, 434–437 (2016). [D. Gershoni]

Optomechanical resonators

• Metzger, C. H. & Karrai, K. Cavity cooling of a microlever. Nature 432, 1002 (2004).
• Arcizet, O., Cohadon, P.-F., Briant, T., Pinard, M. & Heidmann, A. Radiation-pressure cooling and optomechanical instability of a micromirror. Nature 444, 71 (2006). [A. Heidmann]
• Rocheleau, T. et al. Preparation and detection of a mechanical resonator near the ground state of motion. Nature 463, 72–75 (2009). [KC. Schwab]
• O’Connell, A. D. et al. Quantum ground state and single-phonon control of a mechanical resonator. Nature 464, 697–703 (2010). [AN. Cleland]
• Chan, J. et al. Laser cooling of a nanomechanical oscillator into its quantum ground state. Nature 478, 89–92 (2011). [O. Painter]
• Palomaki, T. A., Teufel, J. D., Simmonds, R. W. & Lehnert, K. W. Entangling Mechanical Motion with Microwave Fields. Science 342, 710–713 (2013).
• Satzinger, K. J. et al. Quantum control of surface acoustic-wave phonons. Nature 563, 661–665 (2018). [AN. Cleland]

Time crystals

• Zhang, J. et al. Observation of a discrete time crystal. Nature 543, 217–220 (2017). [C. Monroe]
• Choi, S. et al. Observation of discrete time-crystalline order in a disordered dipolar many-body system. Nature 543, 221–225 (2017). [MD. Lukin]

Universal quantum computation

• Barenco, A. et al. Elementary gates for quantum computation. Phys. Rev. A 52, 3457–3467 (1995). [A. Barenco/CH. Bennett/R. Cleve/DP. DiVincenzo/N. Margolus/P. Shor/T. Sleator/JA. Smolin/H. Weinfurter]
• DiVincenzo, D. P. The Physical Implementation of Quantum Computation. Fort. Phys. 48, 771–783 (2000).
• Bravyi, S. & Kitaev, A. Universal quantum computation with ideal Clifford gates and noisy ancillas. Phys. Rev. A 71, 022316 (2005).
• Broadbent, A., Fitzsimons, J. & Kashefi, E. Universal blind quantum computation. 2009 50th Annual IEEE Symposium on Foundations of Computer Science 517–526 (2009).
• Barz, S. et al. Demonstration of Blind Quantum Computing. Science 335, 303–308 (2012). [P. Walther]

Quantum advantage (supremacy)

• Arute, F. et al. Quantum supremacy using a programmable superconducting processor. Nature 574, 505–510 (2019). [Google]
• Wang, H. et al. Boson Sampling with 20 Input Photons and a 60-Mode Interferometer in a 10¹⁴-Dimensional Hilbert Space. Phys. Rev. Lett. 123, 250503 (2019). [CY. Lu/JW. Pan]

Quantum algorithms

• Shor, P. W. Algorithms for quantum computation: discrete logarithms and factoring. Proceedings 35th Annual Symposium on Foundations of Computer Science 124–134 (1994).
• Grover, L. K. A fast quantum mechanical algorithm for database search. Proceedings of the 28th annual ACM symposium on Theory of Computing - STOC ’96, 212–219 (1996).
• Harrow, A. W., Hassidim, A. & Lloyd, S. Quantum Algorithm for Linear Systems of Equations. Phys. Rev. Lett. 103, 150502 (2009).
• Monz, T. et al. Realization of a scalable Shor algorithm. Science 351, 1068–1070 (2016). [R. Blatt]
• Havlíček, V. et al. Supervised learning with quantum-enhanced feature spaces. Nature 567, 209–212 (2019). [JM. Gambetta]
• Gilyén, A., Su, Y., Low, G. H. & Wiebe, N. Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics. Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing, 193–204 (2019).
• Harrigan, M. P. et al. Quantum approximate optimization of non-planar graph problems on a planar superconducting processor. Nat. Phys. 17, 332-336 (2021). [Google]
• Childs, A. M., Su, Y., Tran, M. C., Wiebe, N. & Zhu, S. Theory of Trotter Error with Commutator Scaling. Phys. Rev. X 11, 011020 (2021).
• Huggins, W. J. et al. Efficient and noise resilient measurements for quantum chemistry on near-term quantum computers. npj Quantum Inf. 7, 23 (2021). [R. Babbush]

Quantum computational complexity

• Yao, A. C.-C. Some complexity questions related to distributive computing. Proc. Annu. ACM Symp. Theory Comput. 209–213 (1979).
• Buhrman, H., Cleve, R., Watrous, J. & de Wolf, R. Quantum Fingerprinting. Phys. Rev. Lett. 87, 167902 (2001).
• Aaronson, S. & Arkhipov, A. The Computational Complexity of Linear Optics. Theory of Computing 9, 143–252 (2011).

Quantum error correction

• Aaronson, S. & Gottesman, D. Improved simulation of stabilizer circuits. Phys. Rev. A 70, 052328 (2004).
• Almheiri, A., Dong, X. & Harlow, D. Bulk locality and quantum error correction in AdS/CFT. J. High Energ. Phys. 2015, 163 (2015).

Quantum simulation

• Vidal, G. Efficient Classical Simulation of Slightly Entangled Quantum Computations. Phys. Rev. Lett. 91, 147902 (2003).
• Vidal, G. Efficient Simulation of One-Dimensional Quantum Many-Body Systems. Phys. Rev. Lett. 93, 040502 (2004).
• Bernien, H. et al. Probing many-body dynamics on a 51-atom quantum simulator. Nature 551, 579–584 (2017). [M. Greiner/V. Vuletic/MD. Lukin]
• Reiher, M., Wiebe, N., Svore, K. M., Wecker, D. & Troyer, M. Elucidating reaction mechanisms on quantum computers. PNAS 114, 7555–7560 (2017).
• Low, G. H. & Chuang, I. L. Optimal Hamiltonian Simulation by Quantum Signal Processing. Phys. Rev. Lett. 118, 010501 (2017).
• Kokail, C. et al. Self-verifying variational quantum simulation of lattice models. Nature 569, 355–360 (2019). [P. Zoller]
• Wang, D., Higgott, O. & Brierley, S. Accelerated Variational Quantum Eigensolver. Phys. Rev. Lett. 122, 140504 (2019).
• Google AI Quantum. Hartree-Fock on a superconducting qubit quantum computer. Science 369, 1084–1089 (2020). [Google]
• Zhou, Y., Stoudenmire, E. M. & Waintal, X. What Limits the Simulation of Quantum Computers? Phys. Rev. X 10, 041038 (2020).
• Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator. Nature 595, 227–232 (2021). [MD. Lukin]
• Scholl, P. et al. Quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms. Nature 595, 233–238 (2021). [A. Browaeys]

Quantum information

• Yao, A. C. Protocols for secure computations. 23rd Annual Symposium on Foundations of Computer Science 160–164 (1982).
• Kitagawa, M. & Ueda, M. Squeezed spin states. Phys. Rev. A 47, 5138–5143 (1993).
• Bollinger, J. J., Itano, W. M., Wineland, D. J. & Heinzen, D. J. Optimal frequency measurements with maximally correlated states. Phys. Rev. A 54, R4649–R4652 (1996).
• Hayden, P. & Preskill, J. Black holes as mirrors: quantum information in random subsystems. J. High Energy Phys. 09(2007)120 (2007).
• Wolf, M. M., Verstraete, F., Hastings, M. B. & Cirac, J. I. Area Laws in Quantum Systems: Mutual Information and Correlations. Phys. Rev. Lett. 100, 070502 (2008).
• Richerme, P. et al. Non-local propagation of correlations in quantum systems with long-range interactions. Nature 511, 198–201 (2014). [C. Monroe]
• Koski, J. V., Kutvonen, A., Khaymovich, I. M., Ala-Nissila, T. & Pekola, J. P. On-Chip Maxwell’s Demon as an Information-Powered Refrigerator. Phys. Rev. Lett. 115, 260602 (2015).
• Landsman, K. A. et al. Verified quantum information scrambling. Nature 567, 61–65 (2019). [C. Monroe]

Bell inequalities

• Einstein, A., Podolsky, B. & Rosen, N. Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Phys. Rev. 47, 777–780 (1935).
• Bell, J. S. On the Einstein Podolsky Rosen paradox. Phys. Phys. Fiz. 1, 195–200 (1964).
• Clauser, J. F., Horne, M. A., Shimony, A. & Holt, R. A. Proposed Experiment to Test Local Hidden-Variable Theories. Phys. Rev. Lett. 23, 880–884 (1969).
• Aspect, A., Grangier, P. & Roger, G. Experimental Tests of Realistic Local Theories via Bell’s Theorem. Phys. Rev. Lett. 47, 460–463 (1981).
• Ansmann, M. et al. Violation of Bell's inequality in Josephson phase qubits. Nature 461, 504–506 (2009). [JM. Martinis]
• Hensen, B. et al. Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres. Nature 526, 682–686 (2015). [R. Hanson]
• Giustina, M. et al. Significant-Loophole-Free Test of Bell’s Theorem with Entangled Photons. Phys. Rev. Lett. 115, 250401 (2015). [A. Zeilinger]
• Shalm, L. K. et al. Strong Loophole-Free Test of Local Realism. Phys. Rev. Lett. 115, 250402 (2015). [SW. Nam]
• Rosenfeld, W. et al. Event-Ready Bell Test Using Entangled Atoms Simultaneously Closing Detection and Locality Loopholes. Phys. Rev. Lett. 119, 010402 (2017). [H. Weinfurter]

Quantum memory

• Maurer, P. C. et al. Room-Temperature Quantum Bit Memory Exceeding One Second. Science 336, 1283–1286 (2012). [MD. Lukin]
• Reagor, M. et al. Quantum memory with millisecond coherence in circuit QED. Phys. Rev. B 94, 014506 (2016). [RJ. Schoelkopf]

Quantum network

• Ritter, S. et al. An elementary quantum network of single atoms in optical cavities. Nature 484, 195–200 (2012). [G. Rempe]
• Kalb, N. et al. Entanglement distillation between solid-state quantum network nodes. Science 356, 928–932 (2017). [R. Hanson]
• Kurpiers, P. et al. Deterministic quantum state transfer and remote entanglement using microwave photons. Nature 558, 264–267 (2018). [A. Wallraff]
• Bienfait, A. et al. Phonon-mediated quantum state transfer and remote qubit entanglement. Science 364, 368–371 (2019). [AN. Cleland]

Quantum communication

• Beveratos, A. et al. Single Photon Quantum Cryptography. Phys. Rev. Lett. 89, 187901 (2002). [P. Grangier]
• Lo, H.-K., Ma, X. & Chen, K. Decoy State Quantum Key Distribution. Phys. Rev. Lett. 94, 230504 (2005).
• Azuma, K., Tamaki, K. & Lo, H.-K. All-photonic quantum repeaters. Nat. Commun. 6, 6787 (2015).
• Yin, J. et al. Satellite-based entanglement distribution over 1200 kilometers. Science 356, 1140–1144 (2017). [CZ. Peng/JY. Wang/JW. Pan]
• Yu, Y. et al. Entanglement of two quantum memories via fibres over dozens of kilometres. Nature 578, 240–245 (2020). [Q. Zhang/XH. Bao/JW. Pan]
• Bhaskar, M. K. et al. Experimental demonstration of memory-enhanced quantum communication. Nature 580, 60-64 (2020). [MD. Lukin]
• Yin, J. et al. Entanglement-based secure quantum cryptography over 1,120 kilometres. Nature 582, 501-505 (2020). [CZ. Peng/AK. Ekert/JW. Pan]
• Fang, X.-T. et al. Implementation of quantum key distribution surpassing the linear rate-transmittance bound. Nat. Photon. 14, 422–425 (2020). [XF. Ma/TY. Chen/JW. Pan]
• Chen, J.-P. et al. Sending-or-Not-Sending with Independent Lasers: Secure Twin-Field Quantum Key Distribution over 509 km. Phys. Rev. Lett. 124, 070501 (2020). [ZB. Wang/Q. Zhang/JW. Pan]

Quantum teleportation

• Bouwmeester, D. et al. Experimental quantum teleportation. Nature 390, 575–579 (1997). [A. Zeilinger]
• Olmschenk, S. et al. Quantum Teleportation Between Distant Matter Qubits. Science 323, 486–489 (2009). [C. Monroe]
• Llewellyn, D. et al. Chip-to-chip quantum teleportation and multi-photon entanglement in silicon. Nat. Phys. 16, 148–153 (2019). [JW. Wang/MG. Thompson]

Quantum coherence

• Viola, L. & Lloyd, S. Dynamical suppression of decoherence in two-state quantum systems. Phys. Rev. A 58, 2733–2744 (1998).

Entanglement

• Briegel, H. J. & Raussendorf, R. Persistent Entanglement in Arrays of Interacting Particles. Phys. Rev. Lett. 86, 910–913 (2001).
• Arnesen, M. C., Bose, S. & Vedral, V. Natural Thermal and Magnetic Entanglement in the 1D Heisenberg Model. Phys. Rev. Lett. 87, 017901 (2001).
• Osborne, T. J. & Nielsen, M. A. Entanglement in a simple quantum phase transition. Phys. Rev. A 66, 032110 (2002).
• Pollmann, F., Turner, A. M., Berg, E. & Oshikawa, M. Entanglement spectrum of a topological phase in one dimension. Phys. Rev. B 81, 064439 (2010).
• Strobel, H. et al. Fisher information and entanglement of non-Gaussian spin states. Science 345, 424–427 (2014). [MK. Oberthaler]
• Brydges, T. et al. Probing Rényi entanglement entropy via randomized measurements. Science 364, 260–263 (2019). [CF. Roos]

Quantum many-body scars

• Turner, C. J., Michailidis, A. A., Abanin, D. A., Serbyn, M. & Papić, Z. Weak ergodicity breaking from quantum many-body scars. Nat. Phys. 14, 745–749 (2018).
• Turner, C. J., Michailidis, A. A., Abanin, D. A., Serbyn, M. & Papić, Z. Quantum scarred eigenstates in a Rydberg atom chain: Entanglement, breakdown of thermalization, and stability to perturbations. Phys. Rev. B 98, 155134 (2018).
• Ho, W. W., Choi, S., Pichler, H. & Lukin, M. D. Periodic Orbits, Entanglement, and Quantum Many-Body Scars in Constrained Models: Matrix Product State Approach. Phys. Rev. Lett. 122, 040603 (2019).
• Choi, S. et al. Emergent SU(2) Dynamics and Perfect Quantum Many-Body Scars. Phys. Rev. Lett. 122, 220603 (2019). [DA. Abanin]

Quantum sensing (with NV)

• Maze, J. R. et al. Nanoscale magnetic sensing with an individual electronic spin in diamond. Nature 455, 644–647 (2008). [MD. Lukin]
• Jarmola, A., Acosta, V. M., Jensen, K., Chemerisov, S. & Budker, D. Temperature- and Magnetic-Field-Dependent Longitudinal Spin Relaxation in Nitrogen-Vacancy Ensembles in Diamond. Phys. Rev. Lett. 108, 197601 (2012).
• Staudacher, T. et al. Nuclear Magnetic Resonance Spectroscopy on a (5-Nanometer)³ Sample Volume. Science 339, 561–563 (2013). [F. Reinhard/J. Wrachtrup]
• Lovchinsky, I. et al. Nuclear magnetic resonance detection and spectroscopy of single proteins using quantum logic. Science 351, 836–841 (2016). [HK. Park/MD. Lukin]
• Du, C. et al. Control and local measurement of the spin chemical potential in a magnetic insulator. Science 357, 195–198 (2017). [A. Yacoby]

(Anderson) Localization

• Anderson, P. W. Absence of Diffusion in Certain Random Lattices. Phys. Rev. 109, 1492–1505 (1958).
• Abrahams, E., Anderson, P. W., Licciardello, D. C. & Ramakrishnan, T. V. Scaling Theory of Localization: Absence of Quantum Diffusion in Two Dimensions. Phys. Rev. Lett. 42, 673–676 (1979).
• John, S. Strong localization of photons in certain disordered dielectric superlattices. Phys. Rev. Lett. 58, 2486–2489 (1987).
• Gornyi, I. V., Mirlin, A. D. & Polyakov, D. G. Interacting Electrons in Disordered Wires: Anderson Localization and Low-T Transport. Phys. Rev. Lett. 95, 206603 (2005).
• Hu, H., Strybulevych, A., Page, J. H., Skipetrov, S. E. & van Tiggelen, B. A. Localization of ultrasound in a three-dimensional elastic network. Nat. Phys. 4, 945–948 (2009).
• Wang, P. et al. Localization and delocalization of light in photonic moiré lattices. Nature 577, 42–46 (2019). [FW. Ye]

Many-body localization

• Basko, D. M., Aleiner, I. L. & Altshuler, B. L. Metal–insulator transition in a weakly interacting many-electron system with localized single-particle states. Ann. Phys. 321, 1126–1205 (2006).
• Oganesyan, V. & Huse, D. A. Localization of interacting fermions at high temperature. Phys. Rev. B 75, 155111 (2007).
• Pal, A. & Huse, D. A. Many-body localization phase transition. Phys. Rev. B 82, 174411 (2010).
• Bardarson, J. H., Pollmann, F. & Moore, J. E. Unbounded Growth of Entanglement in Models of Many-Body Localization. Phys. Rev. Lett. 109, 017202 (2012).
• Serbyn, M., Papić, Z. & Abanin, D. A. Universal Slow Growth of Entanglement in Interacting Strongly Disordered Systems. Phys. Rev. Lett. 110, 260601 (2013).
• Serbyn, M., Papić, Z. & Abanin, D. A. Local Conservation Laws and the Structure of the Many-Body Localized States. Phys. Rev. Lett. 111, 127201 (2013).
• Iyer, S., Oganesyan, V., Refael, G. & Huse, D. A. Many-body localization in a quasiperiodic system. Phys. Rev. B 87, 134202 (2013).
• Huse, D. A., Nandkishore, R., Oganesyan, V., Pal, A. & Sondhi, S. L. Localization-protected quantum order. Phys. Rev. B 88, 014206 (2013).
• Kjäll, J. A., Bardarson, J. H. & Pollmann, F. Many-Body Localization in a Disordered Quantum Ising Chain. Phys. Rev. Lett. 113, 107204 (2014).
• Huse, D. A., Nandkishore, R. & Oganesyan, V. Phenomenology of fully many-body-localized systems. Phys. Rev. B 90, 174202 (2014).
• Schreiber, M. et al. Observation of many-body localization of interacting fermions in a quasirandom optical lattice. Science 349, 842–845 (2015). [I. Bloch]
• Choi, J. et al. Exploring the many-body localization transition in two dimensions. Science 352, 1547–1552 (2016). [C. Gross]
• Smith, J. et al. Many-body localization in a quantum simulator with programmable random disorder. Nat. Phys. 12, 907–911 (2016). [C. Monroe]
• Bordia, P., Lüschen, H., Schneider, U., Knap, M. & Bloch, I. Periodically driving a many-body localized quantum system. Nat. Phys. 13, 460–464 (2017).
• Lüschen, H. P. et al. Signatures of Many-Body Localization in a Controlled Open Quantum System. Phys. Rev. X 7, 011034 (2017). [U. Schneider]
• Wei, K. X., Ramanathan, C. & Cappellaro, P. Exploring Localization in Nuclear Spin Chains. Phys. Rev. Lett. 120, 070501 (2018).
• Rispoli, M. et al. Quantum critical behaviour at the many-body localization transition. Nature 573, 385-389 (2019). [M. Greiner]
• Lukin, A. et al. Probing entanglement in a many-body–localized system. Science 364, 256–260 (2019). [M. Greiner]
• Khemani, V., Hermele, M. & Nandkishore, R. Localization from Hilbert space shattering: From theory to physical realizations. Phys. Rev. B 101, 174204 (2020).

Quantum statistical mechanics

• Deutsch, J. M. Quantum statistical mechanics in a closed system. Phys. Rev. A 43, 2046–2049 (1991).

Thermalization

• Srednicki, M. Chaos and quantum thermalization. Phys. Rev. E 50, 888–901 (1994).
• Rigol, M., Dunjko, V., Yurovsky, V. & Olshanii, M. Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of 1D Lattice Hard-Core Bosons. Phys. Rev. Lett. 98, 050405 (2007).
• Rigol, M., Dunjko, V. & Olshanii, M. Thermalization and its mechanism for generic isolated quantum systems. Nature 452, 854–858 (2008).
• Eckstein, M., Kollar, M. & Werner, P. Thermalization after an Interaction Quench in the Hubbard Model. Phys. Rev. Lett. 103, 056403 (2009).
• Rigol, M. Breakdown of Thermalization in Finite One-Dimensional Systems. Phys. Rev. Lett. 103, 100403 (2009).
• Shiraishi, N. & Mori, T. Systematic Construction of Counterexamples to the Eigenstate Thermalization Hypothesis. Phys. Rev. Lett. 119, 030601 (2017).

Nonequilibrium dynamics

• Kollath, C., Läuchli, A. M. & Altman, E. Quench Dynamics and Nonequilibrium Phase Diagram of the Bose-Hubbard Model. Phys. Rev. Lett. 98, 180601 (2007).

Matrix product states

• Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016).

Neuromorphic computing

• Chua, L. Memristor - The missing circuit element. IEEE Transactions on Circuit Theory 18, 507–519 (1971).
• Strukov, D. B., Snider, G. S., Stewart, D. R. & Williams, R. S. The missing memristor found. Nature 453, 80–83 (2008).
• Pickett, M. D., Medeiros-Ribeiro, G. & Williams, R. S. A scalable neuristor built with Mott memristors. Nat. Mater. 12, 114–117 (2012).

HEMT

• Meneghesso, G. et al. Reliability of GaN High-Electron-Mobility Transistors: State of the Art and Perspectives. IEEE Trans. Device Mater. Reliab. 8, 332–343 (2008). [E. Zanoni]
• Yan, Z., Liu, G., Khan, J. M. & Balandin, A. A. Graphene quilts for thermal management of high-power GaN transistors. Nat. Commun. 3, 827 (2012).

FETs

• Qiu, C. et al. Dirac-source field-effect transistors as energy-efficient, high-performance electronic switches. Science 361, 387–392 (2018). [ZY. Zhang/LM. Peng]
• Li, T. et al. A native oxide high-κ gate dielectric for two-dimensional electronics. Nat. Electron. 3, 473–478 (2020). [HL. Peng]
• Cheema, S. S. et al. Ultrathin ferroic HfO₂–ZrO₂ superlattice gate stack for advanced transistors. Nature 604, 65–71 (2022). [S. Salahuddin]
• Huang, J.-K. et al. High-κ perovskite membranes as insulators for two-dimensional transistors. Nature 605, 262–267 (2022). [LJ. Li/S. Li]

Spintronics

• Appelbaum, I., Huang, B. & Monsma, D. J. Electronic measurement and control of spin transport in silicon. Nature 447, 295–298 (2007).
• Koralek, J. D. et al. Emergence of the persistent spin helix in semiconductor quantum wells. Nature 458, 610–613 (2009). [DD. Awschalom]
• Kajiwara, Y. et al. Transmission of electrical signals by spin-wave interconversion in a magnetic insulator. Nature 464, 262–266 (2010). [E. Saitoh]
• Emori, S., Bauer, U., Ahn, S.-M., Martinez, E. & Beach, G. S. D. Current-driven dynamics of chiral ferromagnetic domain walls. Nat. Mater. 12, 611–616 (2013).
• Cornelissen, L. J., Liu, J., Duine, R. A., Youssef, J. B. & van Wees, B. J. Long-distance transport of magnon spin information in a magnetic insulator at room temperature. Nat. Phys. 11, 1022–1026 (2015).
• Wadley, P. et al. Electrical switching of an antiferromagnet. Science 351, 587–590 (2016). [T. Jungwirth]
• Khymyn, R., Lisenkov, I., Tiberkevich, V., Ivanov, B. A. & Slavin, A. Antiferromagnetic THz-frequency Josephson-like Oscillator Driven by Spin Current. Sci. Rep. 7, 43705 (2017).
• Lebrun, R. et al. Tunable long-distance spin transport in a crystalline antiferromagnetic iron oxide. Nature 561, 222-225 (2018). [M. Kläui]
• Lu, H. et al. Spin-dependent charge transport through 2D chiral hybrid lead-iodide perovskites. Sci. Adv. 5, eaay0571 (2019). [MC. Beard/ZV. Vardeny]
• Li, J. et al. Spin current from sub-terahertz-generated antiferromagnetic magnons. Nature 578, 70–74 (2020). [J. Shi]
• Luo, Z. et al. Current-driven magnetic domain-wall logic. Nature 579, 214–218 (2020). [P. Gambardella/LJ. Heyderman]
• Vaidya, P. et al. Subterahertz spin pumping from an insulating antiferromagnet. Science 368, 160–165 (2020). [E. del Barco]
• Qian, Q. et al. Chiral molecular intercalation superlattices. Nature 606, 902–908 (2022). [XF. Duan]

Single-photon detector

• Korzh, B. et al. Demonstration of sub-3 ps temporal resolution with a superconducting nanowire single-photon detector. Nat. Photon. 14, 250–255 (2020). [KK. Berggren]

Non-Hermitian physics

• Kawabata, K., Shiozaki, K., Ueda, M. & Sato, M. Symmetry and Topology in Non-Hermitian Physics. Phys. Rev. X 9, 041015 (2019).
• Yokomizo, K. & Murakami, S. Non-Bloch Band Theory of Non-Hermitian Systems. Phys. Rev. Lett. 123, 066404 (2019).
• Kawabata, K., Bessho, T. & Sato, M. Classification of Exceptional Points and Non-Hermitian Topological Semimetals. Phys. Rev. Lett. 123, 066405 (2019).
• Hamazaki, R., Kawabata, K. & Ueda, M. Non-Hermitian Many-Body Localization. Phys. Rev. Lett. 123, 090603 (2019).
• Song, F., Yao, S. & Wang, Z. Non-Hermitian Topological Invariants in Real Space. Phys. Rev. Lett. 123, 246801 (2019).
• Xiao, L. et al. Non-Hermitian bulk–boundary correspondence in quantum dynamics. Nat. Phys. 16, 761–766 (2020). [Z. Wang/W. Yi/P. Xue]

Machine learning (materials)

• Raccuglia, P. et al. Machine-learning-assisted materials discovery using failed experiments. Nature 533, 73–76 (2016). [SA. Friedler/J. Schrier/AJ. Norquist]
• Wang, L. Discovering phase transitions with unsupervised learning. Phys. Rev. B 94, 195105 (2016).
• Ward, L., Agrawal, A., Choudhary, A. & Wolverton, C. A general-purpose machine learning framework for predicting properties of inorganic materials. npj Comput. Mater. 2, 16028 (2016).
• Carleo, G. & Troyer, M. Solving the quantum many-body problem with artificial neural networks. Science 355, 602–606 (2017).
• Carrasquilla, J. & Melko, R. G. Machine learning phases of matter. Nat. Phys. 13, 431–434 (2017).
• van Nieuwenburg, E. P. L., Liu, Y.-H. & Huber, S. D. Learning phase transitions by confusion. Nat. Phys. 13, 435–439 (2017).
• Schütt, K. T., Arbabzadah, F., Chmiela, S., Müller, K. R. & Tkatchenko, A. Quantum-chemical insights from deep tensor neural networks. Nat. Commun. 8, 13890 (2017).
• Zhang, Y. & Kim, E.-A. Quantum Loop Topography for Machine Learning. Phys. Rev. Lett. 118, 216401 (2017).
• Wetzel, S. J. Unsupervised learning of phase transitions: From principal component analysis to variational autoencoders. Phys. Rev. E 96, 022140 (2017).
• Zhang, P., Shen, H. & Zhai, H. Machine Learning Topological Invariants with Neural Networks. Phys. Rev. Lett. 120, 066401 (2018).
• Xie, T. & Grossman, J. C. Crystal Graph Convolutional Neural Networks for an Accurate and Interpretable Prediction of Material Properties. Phys. Rev. Lett. 120, 145301 (2018).
• Stanev, V. et al. Machine learning modeling of superconducting critical temperature. npj Comput. Mater. 4, 29 (2018). [I. Takeuchi]
• Rem, B. S. et al. Identifying quantum phase transitions using artificial neural networks on experimental data. Nat. Phys. 15, 917-920 (2019). [K. Sengstock/C. Weitenberg]
• Bapst, V. et al. Unveiling the predictive power of static structure in glassy systems. Nat. Phys. 16, 448–454 (2020). [P. Kohli]
• Choo, K., Neupert, T. & Carleo, G. Two-dimensional frustrated J₁-J₂ model studied with neural network quantum states. Phys. Rev. B 100, 125124 (2019).

Machine learning (physical system)

• Shen, Y. et al. Deep learning with coherent nanophotonic circuits. Nat. Photon. 11, 441–446 (2017). [M. Soljačić]
• Lin, X. et al. All-optical machine learning using diffractive deep neural networks. Science 361, 1004–1008 (2018). [A. Ozcan]
• Cong, I., Choi, S. & Lukin, M. D. Quantum convolutional neural networks. Nat. Phys. 15, 1273-1278 (2019).

Machine learning

• Udrescu, S.-M. & Tegmark, M. AI Feynman: A physics-inspired method for symbolic regression. Sci. Adv. 6, eaay2631 (2020).
• Beer, K. et al. Training deep quantum neural networks. Nat. Commun. 11, 808 (2020). [R. Wolf]
• Iten, R., Metger, T., Wilming, H., del Rio, L. & Renner, R. Discovering Physical Concepts with Neural Networks. Phys. Rev. Lett. 124, 010508 (2020).
• Broughton, M. et al. TensorFlow Quantum: A Software Framework for Quantum Machine Learning. arXiv:2003.02989 [cond-mat, physics:quant-ph] (2020). [M. Mohseni]
• Li, Z. et al. Neural Operator: Graph Kernel Network for Partial Differential Equations. arXiv:2003.03485 [cs, math, stat] (2020). [A. Anandkumar]
• Cranmer, M. et al. Lagrangian Neural Networks. arXiv:2003.04630 [physics, stat] (2020). [S. Ho]
• Li, Z. et al. Fourier Neural Operator for Parametric Partial Differential Equations. arXiv:2010.08895 [cs, math] (2020). [A. Anandkumar]

Phonon measurements

• Thomsen, C., Grahn, H. T., Maris, H. J. & Tauc, J. Surface generation and detection of phonons by picosecond light pulses. Phys. Rev. B 34, 4129–4138 (1986).

Thermal conductivity

• Callaway, J. Model for Lattice Thermal Conductivity at Low Temperatures. Phys. Rev. 113, 1046–1051 (1959).
• Slack, G. A. Nonmetallic crystals with high thermal conductivity. J. Phys. Chem. Solids 34, 321–335 (1972).
• Cahill, D. G. Thermal conductivity measurement from 30 to 750 K: the 3ω method. Rev. Sci. Instrum. 61, 802–808 (1990).
• Chang, C. W., Okawa, D., Majumdar, A. & Zettl, A. Solid-State Thermal Rectifier. Science 314, 1121–1124 (2006).
• Yu, J.-K., Mitrovic, S., Tham, D., Varghese, J. & Heath, J. R. Reduction of thermal conductivity in phononic nanomesh structures. Nat. Nanotechnol. 5, 718-721 (2010).
• Esfarjani, K., Chen, G. & Stokes, H. T. Heat transport in silicon from first-principles calculations. Phys. Rev. B 84, 085204 (2011).
• Wang, Z., Alaniz, J. E., Jang, W., Garay, J. E. & Dames, C. Thermal Conductivity of Nanocrystalline Silicon: Importance of Grain Size and Frequency-Dependent Mean Free Paths. Nano Lett. 11, 2206–2213 (2011).
• Luckyanova, M. N. et al. Coherent Phonon Heat Conduction in Superlattices. Science 338, 936–939 (2012). [G. Chen]
• Losego, M. D., Grady, M. E., Sottos, N. R., Cahill, D. G. & Braun, P. V. Effects of chemical bonding on heat transport across interfaces. Nat. Mater. 11, 502–506 (2012).
• Kucsko, G. et al. Nanometre-scale thermometry in a living cell. Nature 500, 54–58 (2013). [HK. Park/MD. Lukin]
• Ravichandran, J. et al. Crossover from incoherent to coherent phonon scattering in epitaxial oxide superlattices. Nat. Mater. 13, 168–172 (2013). [R. Ramesh/MA. Zurbuchen]
• Johnson, J. A. et al. Direct Measurement of Room-Temperature Nondiffusive Thermal Transport Over Micron Distances in a Silicon Membrane. Phys. Rev. Lett. 110, 025901 (2013).
• Hu, Y., Zeng, L., Minnich, A. J., Dresselhaus, M. S. & Chen, G. Spectral mapping of thermal conductivity through nanoscale ballistic transport. Nat. Nanotechnol. 10, 701–706 (2015).
• Ju, S. et al. Designing Nanostructures for Phonon Transport via Bayesian Optimization. Phys. Rev. X 7, 021024 (2017). [J. Shiomi]
• Chen, K. et al. Ultrahigh thermal conductivity in isotope-enriched cubic boron nitride. Science 367, 555–559 (2020). [D. Broido/G. Chen]

Acoustics

• Fleury, R., Sounas, D. L., Sieck, C. F., Haberman, M. R. & Alù, A. Sound Isolation and Giant Linear Nonreciprocity in a Compact Acoustic Circulator. Science 343, 516–519 (2014).
• Süsstrunk, R. & Huber, S. D. Observation of phononic helical edge states in a mechanical topological insulator. Science 349, 47–50 (2015).
• Ding, Y. et al. Experimental Demonstration of Acoustic Chern Insulators. Phys. Rev. Lett. 122, 014302 (2019). [B. Liang/XF. Zhu/XG. Wan/JC. Chun]

Interferometry

• Caves, C. M. Quantum-mechanical noise in an interferometer. Phys. Rev. D 23, 1693–1708 (1981).
• LIGO Scientific Collaboration. A gravitational wave observatory operating beyond the quantum shot-noise limit. Nat. Phys. 7, 962–965 (2011). [LIGO Collaboration]
• LIGO Scientific Collaboration and Virgo Collaboration. Observation of Gravitational Waves from a Binary Black Hole Merger. Phys. Rev. Lett. 116, 061102 (2016). [LIGO Collaboration]
• Tse, M. et al. Quantum-Enhanced Advanced LIGO Detectors in the Era of Gravitational-Wave Astronomy. Phys. Rev. Lett. 123, 231107 (2019). [LIGO Collaboration]

Dark-matter detection

• Hochberg, Y. et al. Detecting Sub-GeV Dark Matter with Superconducting Nanowires. Phys. Rev. Lett. 123, 151802 (2019). [KK. Berggren]

Optics/Microscopy

• Hong, C. K., Ou, Z. Y. & Mandel, L. Measurement of subpicosecond time intervals between two photons by interference. Phys. Rev. Lett. 59, 2044–2046 (1987).
• Hell, S. W. & Wichmann, J. Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy. Opt. Lett. 19, 780 (1994).
• Pendry, J. B. Negative Refraction Makes a Perfect Lens. Phys. Rev. Lett. 85, 3966–3969 (2000).
• Dudovich, N., Oron, D. & Silberberg, Y. Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy. Nature 418, 512–514 (2002).
• Barnes, W. L., Dereux, A. & Ebbesen, T. W. Surface plasmon subwavelength optics. Nature 424, 824–830 (2003).
• Taubner, T., Korobkin, D., Urzhumov, Y., Shvets, G. & Hillenbrand, R. Near-Field Microscopy Through a SiC Superlens. Science 313, 1595–1595 (2006).
• Betzig, E. et al. Imaging Intracellular Fluorescent Proteins at Nanometer Resolution. Science 313, 1642–1645 (2006). [HF. Hess]
• Cavalieri, A. L. et al. Attosecond spectroscopy in condensed matter. Nature 449, 1029–1032 (2007). [F. Klausz/U. Heinzmann]
• Chen, B.-C. et al. Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution. Science 346, 1257998 (2014). [E. Betzig]
• Luu, T. T. et al. Extreme ultraviolet high-harmonic spectroscopy of solids. Nature 521, 498–502 (2015). [E. Goulielmakis]
• Kealhofer, C. et al. All-optical control and metrology of electron pulses. Science 352, 429–433 (2016). [F. Kransz/P. Baum]
• Zhou, J. et al. Observing crystal nucleation in four dimensions using atomic electron tomography. Nature 570, 500 (2019). [JW. Miao]

Ultrafast phenomena

• Morrison, V. R. et al. A photoinduced metal-like phase of monoclinic VO₂ revealed by ultrafast electron diffraction. Science 346, 445–448 (2014). [BJ. Siwick]
• Wall, S. et al. Ultrafast disordering of vanadium dimers in photoexcited VO₂. Science 362, 572–576 (2018). [O. Delaire/M. Trigo]

Batteries

• Chen, Y. et al. Li metal deposition and stripping in a solid-state battery via Coble creep. Nature 578, 251–255 (2020). [J. Li]
• Yang, B. et al. High-entropy enhanced capacitive energy storage. Nat. Mater. 21, 1074–1080 (2022). [YH. Lin]

High pressure

• Konôpková, Z., McWilliams, R. S., Gómez-Pérez, N. & Goncharov, A. F. Direct measurement of thermal conductivity in solid iron at planetary core conditions. Nature 534, 99–101 (2016).

Magnetism

• Meiklejohn, W. H. & Bean, C. P. New Magnetic Anisotropy. Phys. Rev. 102, 1413–1414 (1956).
• Šmejkal, L., González-Hernández, R., Jungwirth, T. & Sinova, J. Crystal time-reversal symmetry breaking and spontaneous Hall effect in collinear antiferromagnets. Sci. Adv. 6, eaaz8809 (2020).
• Tauchert, S. R. et al. Polarized phonons carry angular momentum in ultrafast demagnetization. Nature 602, 73–77 (2022). [P. Baum]

Molecular magnetism

• Donati, F. et al. Magnetic remanence in single atoms. Science 352, 318–321 (2016). [P. Gambardella/H. Brune]
• Mishra, S. et al. Topological frustration induces unconventional magnetism in a nanographene. Nat. Nanotechnol. 15, 22–28 (2019). [XL. Feng/R. Fasel]

Silicon photonics

• Shen, B., Wang, P., Polson, R. & Menon, R. An integrated-nanophotonics polarization beamsplitter with 2.4 × 2.4 μm² footprint. Nat. Photon. 9, 378–382 (2015).
• Fang, Z. et al. Ultra-low-energy programmable non-volatile silicon photonics based on phase-change materials with graphene heaters. Nat. Nanotechnol. 17, 842–848 (2022). [A. Majumdar]

Polymers

• Noriega, R. et al. A general relationship between disorder, aggregation and charge transport in conjugated polymers. Nat. Mater. 12, 1038–1044 (2013). [A. Salleo]

Neutrinoless double beta decay

• CUORE Collaboration. Improved Limit on Neutrinoless Double-Beta Decay in ¹³⁰Te with CUORE. Phys. Rev. Lett. 124, 122501 (2020).

Industrial cables

• Hartwig, Z. S. et al. VIPER: an industrially scalable high-current high-temperature superconductor cable. Supercond. Sci. Technol. 33, 11LT01 (2020). [ZS. Hartwig]
• Molodyk, A. et al. Development and large volume production of extremely high current density YBa₂Cu₃O₇ superconducting wires for fusion. Sci. Rep. 11, 2084 (2021). [A. Vasiliev]

Miscellaneous

• Nyquist, H. Thermal Agitation of Electric Charge in Conductors. Phys. Rev. 32, 110–113 (1928).
• Simmons, J. G. Generalized Formula for the Electric Tunnel Effect between Similar Electrodes Separated by a Thin Insulating Film. J. Appl. Phys. 34, 1793–1803 (1963).
• Belavin, A. A., Polyakov, A. M. & Zamolodchikov, A. B. Infinite conformal symmetry in two-dimensional quantum field theory. Nuc. Phys. B 241, 333–380 (1984).
• Yablonovitch, E. Inhibited Spontaneous Emission in Solid-State Physics and Electronics. Phys. Rev. Lett. 58, 2059–2062 (1987).
• Allen, P. B. Theory of thermal relaxation of electrons in metals. Phys. Rev. Lett. 59, 1460–1463 (1987).
• Margolus, N. & Levitin, L. B. The maximum speed of dynamical evolution. Phys. D: Nonlinear Phenom. 120, 188–195 (1998).
• Kurs, A. et al. Wireless Power Transfer via Strongly Coupled Magnetic Resonances. Science 317, 83–86 (2007). [M. Soljačić]
• Tisdale, W. A. et al. Hot-Electron Transfer from Semiconductor Nanocrystals. Science 328, 1543–1547 (2010). [DJ. Norris/ES. Aydil/XY. Zhu]
• Cavagna, A. et al. Scale-free correlations in starling flocks. PNAS 107, 11865–11870 (2010). [I. Giardina/G. Parisi]
• Song, Y. M. et al. Digital cameras with designs inspired by the arthropod eye. Nature 497, 95–99 (2013). [JA. Rogers]
• Zhang, W. et al. Tracking excited-state charge and spin dynamics in iron coordination complexes. Nature 509, 345–348 (2014). [KJ. Gaffney]
• Ndabashimiye, G. et al. Solid-state harmonics beyond the atomic limit. Nature 534, 520–523 (2016). [DA. Reis]
• Nova, T. F. et al. An effective magnetic field from optically driven phonons. Nat. Phys. 13, 132–136 (2016). [A. Cavalleri]
• Lu, N. et al. Electric-field control of tri-state phase transformation with a selective dual-ion switch. Nature 546, 124–128 (2017). [J. Wu/P. Yu]
• Kim, K. H. et al. Maxima in the thermodynamic response and correlation functions of deeply supercooled water. Science 358, 1589–1593 (2017). [A. Nilsson]
• Banerjee-Ghosh, K. et al. Separation of enantiomers by their enantiospecific interaction with achiral magnetic substrates. Science 360, 1331–1334 (2018). [R. Naaman/Y. Paltiel]
• Bezginov, N. et al. A measurement of the atomic hydrogen Lamb shift and the proton charge radius. Science 365, 1007–1012 (2019). [EA. Hessels]
• Wang, C. et al. Electromagnetically induced transparency at a chiral exceptional point. Nat. Phys. 16, 334–340 (2020). [L. Yang]

Software

• Azuah, R. T. et al. DAVE: A Comprehensive Software Suite for the Reduction, Visualization, and Analysis of Low Energy Neutron Spectroscopic Data. J. Res. Natl. Inst. 114, 341 (2009).