Giamarchi, T. Quantum Physics in One Dimension (Oxford Univ. Press, 2003).
Lee, P. A., Nagaosa, N. & Wen, X.-G. Doping a Mott insulator: physics of high-temperature superconductivity. Rev. Mod. Phys. 78, 17â85 (2006).
Coleman, P. Theories of non-Fermi liquid behavior in heavy fermions. Phys. B Condens. Matter 259â261, 353â358 (1999).
Stewart, G. R. Non-Fermi-liquid behavior in d– and f-electron metals. Rev. Mod. Phys. 73, 797â855 (2001).
Cao, Y. et al. Strange metal in magic-angle graphene with near Planckian dissipation. Phys. Rev. Lett. 124, 076801 (2020).
Jaoui, A. et al. Quantum critical behaviour in magic-angle twisted bilayer graphene. Nat. Phys. 18, 633â638 (2022).
Wang, P. et al. One-dimensional Luttinger liquids in a two-dimensional moiré lattice. Nature 605, 57â62 (2022).
Yu, G. et al. Evidence for two dimensional anisotropic Luttinger liquids at Millikelvin temperatures. Nat. Commun. 14, 7025 (2023).
Jackiw, R. & Rebbi, C. Solitons with fermion number ½. Phys. Rev. D 13, 3398â3409 (1976).
Su, W. P., Schrieffer, J. R. & Heeger, A. J. Solitons in polyacetylene. Phys. Rev. Lett. 42, 1698â1701 (1979).
Tsui, D. C., Stormer, H. L. & Gossard, A. C. Two-dimensional magnetotransport in the extreme quantum limit. Phys. Rev. Lett. 48, 1559â1562 (1982).
Arovas, D., Schrieffer, J. R. & Wilczek, F. Fractional statistics and the quantum Hall effect. Phys. Rev. Lett. 53, 722â723 (1984).
Stern, A. Anyons and the quantum Hall effectâa pedagogical review. Ann. Phys. 323, 204â249 (2008).
Nayak, C., Simon, S. H., Stern, A., Freedman, M. & Das Sarma, S. Non-Abelian anyons and topological quantum computation. Rev. Mod. Phys. 80, 1083â1159 (2008).
Anderson, P. W. Resonating valence bonds: a new kind of insulator? Mater. Res. Bull. 8, 153â160 (1973). This paper proposed the RVB state, which initiated the research of spin liquids.
Anderson, P. W. The resonating valence bond state in La2CuO4 and superconductivity. Science 235, 1196â1198 (1987).
Moessner, R. & Sondhi, S. L. Resonating valence bond phase in the triangular lattice quantum dimer model. Phys. Rev. Lett. 86, 1881â1884 (2001). This paper concluded the search for an RVB liquid by demonstrating its existence in a microscopic model.
Moessner, R. & Moore, J. E. Topological Phases of Matter (Cambridge Univ. Press, 2021).
Kitaev, A. Y. Fault-tolerant quantum computation by anyons. Ann. Phys. 303, 2â30 (2003).
Wen, X.-G. Quantum orders and symmetric spin liquids. Phys. Rev. B 65, 165113 (2002).
Read, N. & Chakraborty, B. Statistics of the excitations of the resonating-valence-bond state. Phys. Rev. B 40, 7133â7140 (1989).
Kalmeyer, V. & Laughlin, R. B. Equivalence of the resonating-valence-bond and fractional quantum Hall states. Phys. Rev. Lett. 59, 2095â2098 (1987).
Pace, S. D., Morampudi, S. C., Moessner, R. & Laumann, C. R. Emergent fine structure constant of quantum spin ice is large. Phys. Rev. Lett. 127, 117205 (2021).
Hermele, M. et al. Stability of U(1) spin liquids in two dimensions. Phys. Rev. B 70, 214437 (2004).
Lee, S.-S. Stability of the U(1) spin liquid with a spinon Fermi surface in 2+1 dimensions. Phys. Rev. B 78, 085129 (2008).
Huse, D. A., Krauth, W., Moessner, R. & Sondhi, S. L. Coulomb and liquid dimer models in three dimensions. Phys. Rev. Lett. 91, 167004 (2003).
Hermele, M., Fisher, M. P. A. & Balents, L. Pyrochlore photons: the U(1) spin liquid in a Sâ=â1/2 three-dimensional frustrated magnet. Phys. Rev. B 69, 064404 (2004).
Castelnovo, C., Moessner, R. & Sondhi, S. L. Magnetic monopoles in spin ice. Nature 451, 42â45 (2008).
Ng, T.-K. & Lee, P. A. Power-law conductivity inside the Mott gap: application to κ-(BEDTâTTF)2Cu2(CN)3. Phys. Rev. Lett. 99, 156402 (2007).
Motrunich, O. I. Orbital magnetic field effects in spin liquid with spinon Fermi sea: possible application to κ-(ET)2 (Cu)2(CN)3. Phys. Rev. B 73, 155115 (2006). This paper predicted spinon Landau quantization in magnetic fields, a key step in the search for neutral fermions using quantum oscillations.
Sodemann, I., Chowdhury, D. & Senthil, T. Quantum oscillations in insulators with neutral Fermi surfaces. Phys. Rev. B 97, 045152 (2018). This paper developed a theory of quantum oscillations in observables such as resistance and magnetization induced by spinon Landau quantization.
Rao, P. & Sodemann, I. Cyclotron resonance inside the Mott gap: a fingerprint of emergent neutral fermions. Phys. Rev. B 100, 155150 (2019).
Khoo, J. Y., Pientka, F., Lee, P. A. & Villadiego, I. S. Probing the quantum noise of the spinon Fermi surface with NV centers. Phys. Rev. B 106, 115108 (2022).
Jérome, D., Rice, T. M. & Kohn, W. Excitonic insulator. Phys. Rev. 158, 462â475 (1967).
Kohn, W. Excitonic phases. Phys. Rev. Lett. 19, 439â442 (1967).
Blatt, J. M., Böer, K. W. & Brandt, W. Bose-Einstein condensation of excitons. Phys. Rev. 126, 1691â1692 (1962).
Mott, N. F. The transition to the metallic state. Philos. Mag. 6, 287â309 (1961).
Halperin, B. I. & Rice, T. M. Possible anomalies at a semimetal-semiconductor transition. Rev. Mod. Phys. 40, 755â766 (1968).
Kwan, Y. H., Devakul, T., Sondhi, S. L. & Parameswaran, S. A. Theory of competing excitonic orders in insulating WTe2 monolayers. Phys. Rev. B 104, 125133 (2021).
Wang, Y.-Q., Papaj, M. & Moore, J. E. Breakdown of helical edge state topologically protected conductance in time-reversal-breaking excitonic insulators. Phys. Rev. B 108, 205420 (2023).
Hu, Y., Venderbos, J. W. F. & Kane, C. L. Fractional excitonic insulator. Phys. Rev. Lett. 121, 126601 (2018).
Chowdhury, D., Sodemann, I. & Senthil, T. Mixed-valence insulators with neutral Fermi surfaces. Nat. Commun. 9, 1766 (2018).
Xu, X., Yao, W., Xiao, D. & Heinz, T. F. Spin and pseudospins in layered transition metal dichalcogenides. Nat. Phys. 10, 343â350 (2014).
Wang, G. et al. Colloquium: excitons in atomically thin transition metal dichalcogenides. Rev. Mod. Phys. 90, 021001 (2018).
Eisenstein, J. P. Exciton condensation in bilayer quantum Hall systems. Annu. Rev. Condens. Matter Phys. 5, 159â181 (2014).
Liu, X., Watanabe, K., Taniguchi, T., Halperin, B. I. & Kim, P. Quantum Hall drag of exciton condensate in graphene. Nat. Phys. 13, 746â750 (2017).
Li, J. I. A., Taniguchi, T., Watanabe, K., Hone, J. & Dean, C. R. Excitonic superfluid phase in double bilayer graphene. Nat. Phys. 13, 751â755 (2017).
Du, L. et al. Evidence for a topological excitonic insulator in InAs/GaSb bilayers. Nat. Commun. 8, 1971 (2017).
Yu, W. et al. Anomalously large resistance at the charge neutrality point in a zero-gap InAs/GaSb bilayer. New J. Phys. 20, 053062 (2018).
Chen, D. et al. Excitonic insulator in a heterojunction moiré superlattice. Nat. Phys. 18, 1171â1176 (2022).
Zhang, Z. et al. Correlated interlayer exciton insulator in heterostructures of monolayer WSe2 and moiré WS2/WSe2. Nat. Phys. 18, 1214â1220 (2022).
Ma, L. et al. Strongly correlated excitonic insulator in atomic double layers. Nature 598, 585â589 (2021).
Cercellier, H. et al. Evidence for an excitonic insulator phase in 1T TiSe2. Phys. Rev. Lett. 99, 146403 (2007).
Kogar, A. et al. Signatures of exciton condensation in a transition metal dichalcogenide. Science 358, 1314â1317 (2017).
Campbell, D. J. et al. Intrinsic insulating ground state in transition metal dichalcogenide TiSe2. Phys. Rev. Mater. 3, 053402 (2019).
Li, Z. et al. Possible excitonic insulating phase in quantum-confined Sb nanoflakes. Nano Lett. 19, 4960â4964 (2019).
Wakisaka, Y. et al. Excitonic insulator state in Ta2NiSe5 probed by photoemission spectroscopy. Phys. Rev. Lett. 103, 026402 (2009).
Lu, Y. F. et al. Zero-gap semiconductor to excitonic insulator transition in Ta2NiSe5. Nat. Commun. 8, 14408 (2017).
Fukutani, K. et al. Electrical tuning of the excitonic insulator ground state of Ta2NiSe5. Phys. Rev. Lett. 123, 206401 (2019).
Werdehausen, D. et al. Coherent order parameter oscillations in the ground state of the excitonic insulator Ta2NiSe5. Sci. Adv. 4, eaap8652 (2018).
Baldini, E. et al. The spontaneous symmetry breaking in Ta2NiSe5 is structural in nature. Proc. Natl Acad. Sci. USA 120, e2221688120 (2023).
Hossain, M. S. et al. Discovery of a topological exciton insulator with tunable momentum order. Preprint at https://arxiv.org/abs/2312.15862 (2023).
Huang, J. et al. Evidence for an excitonic insulator state in Ta2Pd3Te5. Phys. Rev. X 14, 011046 (2024).
Jia, Y. et al. Evidence for a monolayer excitonic insulator. Nat. Phys. 18, 87â93 (2022). This paper, together with ref. 65, identified a 2D natural crystal (monolayer WTe2) as an excitonic insulator.
Sun, B. et al. Evidence for equilibrium exciton condensation in monolayer WTe2. Nat. Phys. 18, 94â99 (2022). This paper, together with ref. 64, identified a 2D natural crystal (monolayer WTe2) as an excitonic insulator.
Lee, P. A. Quantum oscillations in the activated conductivity in excitonic insulators: possible application to monolayer WTe2. Phys. Rev. B 103, L041101 (2021).
Qian, X., Liu, J., Fu, L. & Li, J. Quantum spin Hall effect in two-dimensional transition metal dichalcogenides. Science 346, 1344â1347 (2014).
Fei, Z. et al. Edge conduction in monolayer WTe2. Nat. Phys. 13, 677â682 (2017).
Tang, S. et al. Quantum spin Hall state in monolayer 1Tâ²-WTe2. Nat. Phys. https://doi.org/10.1038/nphys4174 (2017).
Wu, S. et al. Observation of the quantum spin Hall effect up to 100âkelvin in a monolayer crystal. Science 359, 76â79 (2018).
Fatemi, V. et al. Electrically tunable low-density superconductivity in a monolayer topological insulator. Science 362, 926â929 (2018).
Sajadi, E. et al. Gate-induced superconductivity in a monolayer topological insulator. Science 362, 922â925 (2018).
Wang, P. et al. Landau quantization and highly mobile fermions in an insulator. Nature 589, 225â229 (2021). This paper, together with ref. 74, reported quantum oscillations in monolayer WTe2 insulator.
Tang, Y. et al. Sign-alternating thermoelectric quantum oscillations and insulating Landau levels in monolayer WTe2. Preprint at https://arxiv.org/abs/2405.09665 (2024). This paper, together with ref. 73, reported quantum oscillations in monolayer WTe2 insulator.
Song, T. et al. Unconventional superconducting quantum criticality in monolayer WTe2. Nat. Phys. 20, 269â274 (2024).
He, W.-Y. & Lee, P. A. Electronic density of states of a U(1) quantum spin liquid with spinon Fermi surface. I. Orbital magnetic field effects. Phys. Rev. B 107, 195155 (2023).
Zhou, Y., Kanoda, K. & Ng, T.-K. Quantum spin liquid states. Rev. Mod. Phys. 89, 025003 (2017).
Broholm, C. et al. Quantum spin liquids. Science 367, eaay0668 (2020).
Knolle, J. & Moessner, R. A field guide to spin liquids. Annu. Rev. Condens. Matter Phys. 10, 451â472 (2019).
Takagi, H., Takayama, T., Jackeli, G., Khaliullin, G. & Nagler, S. E. Concept and realization of Kitaev quantum spin liquids. Nat. Rev. Phys. 1, 264â280 (2019).
Savary, L. & Balents, L. Quantum spin liquids: a review. Rep. Prog. Phys. 80, 016502 (2017).
Law, K. T. & Lee, P. A. 1T-TaS2 as a quantum spin liquid. Proc. Natl Acad. Sci. USA 114, 6996â7000 (2017).
He, W.-Y., Xu, X. Y., Chen, G., Law, K. T. & Lee, P. A. Spinon Fermi surface in a cluster Mott insulator model on a triangular lattice and possible application to 1T-TaS2. Phys. Rev. Lett. 121, 046401 (2018).
Sipos, B. et al. From Mott state to superconductivity in 1T-TaS2. Nat. Mater. 7, 960â965 (2008).
Yu, Y. et al. Gate-tunable phase transitions in thin flakes of 1T-TaS2. Nat. Nanotechnol. 10, 270â276 (2015).
Wang, Y. D. et al. Band insulator to Mott insulator transition in 1T-TaS2. Nat. Commun. 11, 4215 (2020).
Ritschel, T., Berger, H. & Geck, J. Stacking-driven gap formation in layered 1T-TaS2. Phys. Rev. B 98, 195134 (2018).
Wu, Z. et al. Effect of stacking order on the electronic state of 1T-TaS2. Phys. Rev. B 105, 035109 (2022).
Chen, Y. et al. Strong correlations and orbital texture in single-layer 1T-TaSe2. Nat. Phys. 16, 218â224 (2020).
Ruan, W. et al. Evidence for quantum spin liquid behaviour in single-layer 1T-TaSe2 from scanning tunnelling microscopy. Nat. Phys. 17, 1154â1161 (2021).
Chen, Y. et al. Evidence for a spinon Kondo effect in cobalt atoms on single-layer 1T-TaSe2. Nat. Phys. 18, 1335â1340 (2022).
Zhang, Q. et al. Quantum spin liquid signatures in monolayer 1T-NbSe2. Nat. Commun. 15, 2336 (2024).
Liu, L. et al. Direct identification of Mott Hubbard band pattern beyond charge density wave superlattice in monolayer 1T-NbSe2. Nat. Commun. 12, 1978 (2021).
Liu, M. et al. Monolayer 1T-NbSe2 as a 2D-correlated magnetic insulator. Sci. Adv. 7, eabi6339 (2021).
Nakata, Y. et al. Monolayer 1T-NbSe2 as a Mott insulator. NPG Asia Mater. 8, e321âe321 (2016).
Kitaev, A. Anyons in an exactly solved model and beyond. Ann. Phys. 321, 2â111 (2006). This paper provided an exactly solvable model for quantum spin liquids.
Jackeli, G. & Khaliullin, G. Mott insulators in the strong spin-orbit coupling limit: from Heisenberg to a quantum compass and Kitaev models. Phys. Rev. Lett. 102, 017205 (2009).
Banerjee, A. et al. Proximate Kitaev quantum spin liquid behaviour in a honeycomb magnet. Nat. Mater. 15, 733â740 (2016).
Plumb, K. W. et al. α-RuCl3: a spin-orbit assisted Mott insulator on a honeycomb lattice. Phys. Rev. B 90, 041112 (2014).
Leahy, I. A. et al. Anomalous thermal conductivity and magnetic torque response in the honeycomb magnet α-RuCl3. Phys. Rev. Lett. 118, 187203 (2017).
Banerjee, A. et al. Excitations in the field-induced quantum spin liquid state of α-RuCl3. npj Quantum Mater. 3, 8 (2018).
Hentrich, R. et al. Unusual phonon heat transport in α-RuCl3: strong spin-phonon scattering and field-induced spin gap. Phys. Rev. Lett. 120, 117204 (2018).
McClarty, P. A. et al. Topological magnons in Kitaev magnets at high fields. Phys. Rev. B 98, 060404 (2018).
Joshi, D. G. Topological excitations in the ferromagnetic Kitaev-Heisenberg model. Phys. Rev. B 98, 060405 (2018).
Gordon, J. S., Catuneanu, A., Sørensen, E. S. & Kee, H.-Y. Theory of the field-revealed Kitaev spin liquid. Nat. Commun. 10, 2470 (2019).
Hickey, C. & Trebst, S. Emergence of a field-driven U(1) spin liquid in the Kitaev honeycomb model. Nat. Commun. 10, 530 (2019).
Ponomaryov, A. N. et al. Nature of magnetic excitations in the high-field phase of α-RuCl3. Phys. Rev. Lett. 125, 037202 (2020).
Wang, Z. et al. Magnetic excitations and continuum of a possibly field-induced quantum spin liquid in α-RuCl3. Phys. Rev. Lett. 119, 227202 (2017).
Czajka, P. et al. Planar thermal Hall effect of topological bosons in the Kitaev magnet α-RuCl3. Nat. Mater. 22, 36â41 (2023). This paper reported the thermal Hall data incompatible with the half-quantization expected for the Majorana transport in α-RuCl3.
Czajka, P. et al. Oscillations of the thermal conductivity in the spin-liquid state of α-RuCl3. Nat. Phys. 17, 915â919 (2021). This paper reported the magneto-oscillations in the thermal conductivity of α-RuCl3.
Kasahara, Y. et al. Majorana quantization and half-integer thermal quantum Hall effect in a Kitaev spin liquid. Nature 559, 227â231 (2018).
Yokoi, T. et al. Half-integer quantized anomalous thermal Hall effect in the Kitaev material candidate α-RuCl3. Science 373, 568â572 (2021).
Zhang, E. Z., Chern, L. E. & Kim, Y. B. Topological magnons for thermal Hall transport in frustrated magnets with bond-dependent interactions. Phys. Rev. B 103, 174402 (2021).
Bruin, J. A. N. et al. Robustness of the thermal Hall effect close to half-quantization in α-RuCl3. Nat. Phys. 18, 401â405 (2022).
Villadiego, I. S. Pseudoscalar U(1) spin liquids in α-RuCl3. Phys. Rev. B 104, 195149 (2021).
Bruin, J. A. N. et al. Origin of oscillatory structures in the magnetothermal conductivity of the putative Kitaev magnet α-RuCl3. APL Mater. 10, 090703 (2022).
Kubota, Y., Tanaka, H., Ono, T., Narumi, Y. & Kindo, K. Successive magnetic phase transitions in α-RuCl3: XY-like frustrated magnet on the honeycomb lattice. Phys. Rev. B 91, 094422 (2015).
Cao, H. B. et al. Low-temperature crystal and magnetic structure of α-RuCl3. Phys. Rev. B 93, 134423 (2016).
Lefrançois, Ã. et al. Oscillations in the magnetothermal conductivity of αâRuCl3: evidence of transition anomalies. Phys. Rev. B 107, 064408 (2023).
Zhang, H. et al. Sample-dependent and sample-independent thermal transport properties of α-RuCl3. Phys. Rev. Mater. 7, 114403 (2023).
Zhang, H. et al. Stacking disorder and thermal transport properties of α-RuCl3. Phys. Rev. Mater. 8, 014402 (2024).
Zhang, H. et al. Anisotropy of thermal conductivity oscillations in relation to the Kitaev spin liquid phase. Preprint at https://arxiv.org/abs/2310.03917 (2023).
Hong, X. et al. Phonon thermal transport shaped by strong spin-phonon scattering in a Kitaev material Na2Co2TeO6. npj Quantum Mater. 9, 18 (2024).
Hong, X. et al. Spinon heat transport in the three-dimensional quantum magnet PbCuTe2O6. Phys. Rev. Lett. 131, 256701 (2023).
Yamashita, M. et al. Presence and absence of itinerant gapless excitations in the quantum spin liquid candidate EtMe2Sb[Pd(dmit)2]2. Phys. Rev. B 101, 140407 (2020).
Ni, J. M. et al. Absence of magnetic thermal conductivity in the quantum spin liquid candidate EtNe3Sb[Pd(dmit)2]2. Phys. Rev. Lett. 123, 247204 (2019).
Bourgeois-Hope, P. et al. Thermal conductivity of the quantum spin liquid candidate EtMe3Sb[Pd(dnit)2]2: no evidence of mobile gapless excitations. Phys. Rev. X 9, 041051 (2019).
Ioffe, L. B. & Larkin, A. I. Gapless fermions and gauge fields in dielectrics. Phys. Rev. B 39, 8988â8999 (1989). This paper developed the so-called Ioffe-Larkin rule, which is important for understanding response functions of fractionalized systems.
Lee, P. A. & Nagaosa, N. Gauge theory of the normal state of high-Tc superconductors. Phys. Rev. B 46, 5621â5639 (1992).
He, W.-Y. & Lee, P. A. Electronic density of states of a U1 quantum spin liquid with spinon Fermi surface. I. Orbital magnetic field effects. Phys. Rev. B 107, 195155 (2023).
Tan, B. S. et al. Unconventional Fermi surface in an insulating state. Science 349, 287â290 (2015).
Li, G. et al. Two-dimensional Fermi surfaces in Kondo insulator SmB6. Science 346, 1208â1212 (2014).
Xiang, Z. et al. Quantum oscillations of electrical resistivity in an insulator. Science 362, 65â69 (2018).
Han, Z., Li, T., Zhang, L., Sullivan, G. & Du, R.-R. Anomalous conductance oscillations in the hybridization gap of InAs/GaSb quantum wells. Phys. Rev. Lett. 123, 126803 (2019).
Xiao, D., Liu, C.-X., Samarth, N. & Hu, L.-H. Anomalous quantum oscillations of interacting electron-hole gases in inverted type-II InAs/GaSb quantum wells. Phys. Rev. Lett. 122, 186802 (2019).
Zheng, G. et al. Unconventional magnetic oscillations in Kagome Mott insulators. Preprint at arXiv https://arxiv.org/abs/2310.07989 (2023).
Li, L., Sun, K., Kurdak, C. & Allen, J. W. Emergent mystery in the Kondo insulator samarium hexaboride. Nat. Rev. Phys. 2, 463â479 (2020).
Shen, H. & Fu, L. Quantum oscillation from in-gap states and a non-Hermitian Landau level problem. Phys. Rev. Lett. 121, 026403 (2018).
Zhang, L., Song, X.-Y. & Wang, F. Quantum oscillation in narrow-gap topological insulators. Phys. Rev. Lett. 116, 046404 (2016).
Ram, P. & Kumar, B. Theory of quantum oscillations of magnetization in Kondo insulators. Phys. Rev. B 96, 075115 (2017).
Knolle, J. & Cooper, N. R. Quantum oscillations without a Fermi surface and the anomalous de Haasâvan Alphen effect. Phys. Rev. Lett. 115, 146401 (2015).
Knolle, J. & Cooper, N. R. Anomalous de Haasâvan Alphen effect in InAs/GaSb quantum wells. Phys. Rev. Lett. 118, 176801 (2017).
Erten, O., Chang, P.-Y., Coleman, P. & Tsvelik, A. M. Skyrme insulators: insulators at the brink of superconductivity. Phys. Rev. Lett. 119, 057603 (2017).
He, W.-Y. & Lee, P. A. Quantum oscillation of thermally activated conductivity in a monolayer WTe2-like excitonic insulator. Phys. Rev. B 104, L041110 (2021).
Zhu, J., Li, T., Young, A. F., Shan, J. & Mak, K. F. Quantum oscillations in 2D insulators induced by graphite gates. Phys. Rev. Lett. 127, 247702 (2021).
Cooper, N. R. & Kelsall, J. Quantum oscillations in an impurity-band Anderson insulator. Sci. Post Phys.15, 118 (2023).
Pirie, H. et al. Visualizing the atomic-scale origin of metallic behavior in Kondo insulators. Science 379, 1214â1218 (2023).
Pal, H. K., Piéchon, F., Fuchs, J.-N., Goerbig, M. & Montambaux, G. Chemical potential asymmetry and quantum oscillations in insulators. Phys. Rev. B 94, 125140 (2016).
Singh, G. & Pal, H. K. Effect of many-body interaction on de Haasâvan Alphen oscillations in insulators. Phys. Rev. B 108, L201103 (2023).
Wu, S. The detection of unconventional quantum oscillations in insulating 2D materials. 2D Mater. 11, 033004 (2024).
Checkelsky, J. G. & Ong, N. P. Thermopower and Nernst effect in graphene in a magnetic field. Phys. Rev. B 80, 81413 (2009).
Zuev, Y. M., Chang, W. & Kim, P. Thermoelectric and magnetothermoelectric transport measurements of graphene. Phys. Rev. Lett. 102, 96807 (2009).
Ni, D., Gui, X., Powderly, K. M. & Cava, R. J. Honeycombâstructure RuI3, a new quantum material related to αâRuCl3. Adv. Mater. 34, e2106831 (2022).
Zhong, R., Gao, T., Ong, N. P. & Cava, R. J. Weak-field induced nonmagnetic state in a Co-based honeycomb. Sci. Adv. 6, eaay6953 (2020).
Zhang, X. et al. A magnetic continuum in the cobalt-based honeycomb magnet BaCo2(AsO4)2. Nat. Mater. 22, 58â63 (2023).
Halloran, T. et al. Geometrical frustration versus Kitaev interactions in BaCo2(AsO4)2. Proc. Natl Acad. Sci. USA 120, e2215509119 (2023).
Onyszczak, M. et al. A platform for far-infrared spectroscopy of quantum materials at millikelvin temperatures. Rev. Sci. Instrum. 94, 103903 (2023).
Potter, A. C., Senthil, T. & Lee, P. A. Mechanisms for sub-gap optical conductivity in Herbertsmithite. Phys. Rev. B 87, 245106 (2013).
Wan, Y. & Armitage, N. P. Resolving continua of fractional excitations by spinon echo in THz 2D coherent spectroscopy. Phys. Rev. Lett. 122, 257401 (2019).
Hart, O. & Nandkishore, R. Extracting spinon self-energies from two-dimensional coherent spectroscopy. Phys. Rev. B 107, 205143 (2023).
Gao, Q., Liu, Y., Liao, H. & Wan, Y. Two-dimensional coherent spectrum of interacting spinons from matrix product states. Phys. Rev. B 107, 165121 (2023).
Chatterjee, S., Rodriguez-Nieva, J. F. & Demler, E. Diagnosing phases of magnetic insulators via noise magnetometry with spin qubits. Phys. Rev. B 99, 104425 (2019).
Khoo, J. Y., Pientka, F. & Sodemann, I. The universal shear conductivity of Fermi liquids and spinon Fermi surface states and its detection via spin qubit noise magnetometry. New J. Phys. 23, 113009 (2021).
Lee, P. A. & Morampudi, S. Proposal to detect emergent gauge field and its Meissner effect in spin liquids using NV centers. Phys. Rev. B 107, 195102 (2023).
Han, W., Maekawa, S. & Xie, X.-C. Spin current as a probe of quantum materials. Nat. Mater. 19, 139â152 (2020).
Park, H. et al. Observation of fractionally quantized anomalous Hall effect. Nature 622, 74â79 (2023). This paper reported the fractional quantum anomalous Hall effect.
Xu, F. et al. Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2. Phys. Rev. X 13, 031037 (2023).
Lu, Z. et al. Fractional quantum anomalous Hall effect in multilayer graphene. Nature 626, 759â764 (2024).
Anderson, E. et al. Programming correlated magnetic states with gate-controlled moiré geometry. Science 381, 325â330 (2023).
Cai, J. et al. Signatures of fractional quantum anomalous Hall states in twisted MoTe2. Nature 622, 63â68 (2023).
Zeng, Y. et al. Thermodynamic evidence of fractional Chern insulator in moiré MoTe2. Nature 622, 69â73 (2023).
Neupert, T., Santos, L., Chamon, C. & Mudry, C. Fractional quantum Hall states at zero magnetic field. Phys. Rev. Lett. 106, 236804 (2011).
Sheng, D. N., Gu, Z.-C., Sun, K. & Sheng, L. Fractional quantum Hall effect in the absence of Landau levels. Nat. Commun. 2, 389 (2011).
Regnault, N. & Bernevig, B. A. Fractional Chern insulator. Phys. Rev. X 1, 021014 (2011).
Tang, E., Mei, J.-W. & Wen, X.-G. High-temperature fractional quantum Hall states. Phys. Rev. Lett. 106, 236802 (2011).
Sun, K., Gu, Z., Katsura, H. & Das Sarma, S. Nearly flatbands with nontrivial topology. Phys. Rev. Lett. 106, 236803 (2011).
Baird, D., Hughes, R. I. G. & Nordmann, A. Heinrich Hertz: Classical Physicist, Modern Philosopher (Springer-Verlag, 1998).
Laumann, C. R. & Moessner, R. Hybrid dyons, inverted Lorentz force, and magnetic Nernst effect in quantum spin ice. Phys. Rev. B 108, L220402 (2023). This paper predicted a novel variant of the Nernst effect in insulators induced by physics of quantum spin ice.
