Keldysh, L. & Kopaev, Y. Possible instability of semimetallic state toward Coulomb interaction. Sov. Phys. Solid State 6, 2219–2224 (1964).


Google Scholar
 

Cloizeaux, J. D. Exciton instability and crystallographic anomalies in semiconductors. J. Phys. Chem. Solids 26, 259–266 (1965).

Article 

Google Scholar
 

Jerome, D., Rice, T. M. & Kohn, W. Excitonic insulator. Phys. Rev. 158, 462–475 (1967).

Article 

Google Scholar
 

Halperin, B. I. & Rice, T. M. Possible anomalies at a semimetal–semiconductor transition. Rev. Mod. Phys. 40, 755–766 (1968).

Article 

Google Scholar
 

Snoke, D. Spontaneous Bose coherence of excitons and polaritons. Science 298, 1368–1372 (2002).

Article 

Google Scholar
 

Batista, C. D., Gubernatis, J. E., Bonča, J. & Lin, H. Q. Intermediate coupling theory of electronic ferroelectricity. Phys. Rev. Lett. 92, 187601 (2004).

Article 

Google Scholar
 

Mazza, G. & Georges, A. Superradiant quantum materials. Phys. Rev. Lett. 122, 017401 (2019).

Article 

Google Scholar
 

Safaei, S. & Mazziotti, D. A. Quantum signature of exciton condensation. Phys. Rev. B 98, 045122 (2018).

Article 

Google Scholar
 

Schouten, A. O., Sager-Smith, L. M. & Mazziotti, D. A. Large cumulant eigenvalue as a signature of exciton condensation. Phys. Rev. B 105, 245151 (2022).

Article 

Google Scholar
 

Baldini, E. et al. The spontaneous symmetry breaking in Ta2NiSe5 is structural in nature. Proc. Natl Acad. Sci. USA 120, e2221688120 (2023).

Article 

Google Scholar
 

Rohwer, T. et al. Collapse of long-range charge order tracked by time-resolved photoemission at high momenta. Nature 471, 490–493 (2011).

Article 

Google Scholar
 

Kogar, A. et al. Signatures of exciton condensation in a transition metal dichalcogenide. Science 358, 1314–1317 (2017).

Article 

Google Scholar
 

Lu, Y. F. et al. Zero-gap semiconductor to excitonic insulator transition in Ta2NiSe5. Nat. Commun. 8, 14408 (2017).

Article 

Google Scholar
 

Werdehausen, D. et al. Coherent order parameter oscillations in the ground state of the excitonic insulator Ta2NiSe5. Sci. Adv. 4, eaap8652 (2018).

Article 

Google Scholar
 

Varsano, D. et al. Carbon nanotubes as excitonic insulators. Nat. Commun. 8, 1461 (2017).

Article 

Google Scholar
 

Ataei, S. S., Varsano, D., Molinari, E. & Rontani, M. Evidence of ideal excitonic insulator in bulk MoS2 under pressure. Proc. Natl Acad. Sci. USA 118, e2010110118 (2021).

Article 

Google Scholar
 

Mazza, G. et al. Nature of symmetry breaking at the excitonic insulator transition: Ta2NiSe5. Phys. Rev. Lett. 124, 197601 (2020).

Article 

Google Scholar
 

Subedi, A. et al. Orthorhombic-to-monoclinic transition in Ta2NiSe5 due to a zone-center optical phonon instability. Phys. Rev. Mater. 4, 083601 (2020).

Article 

Google Scholar
 

Watson, M. D. et al. Band hybridization at the semimetal-semiconductor transition of Ta2NiSe5 enabled by mirror-symmetry breaking. Phys. Rev. Res. 2, 013236 (2020).

Article 

Google Scholar
 

Eisenstein, J. P. & MacDonald, A. H. Bose–Einstein condensation of excitons in bilayer electron systems. Nature 432, 691–694 (2004).

Article 

Google Scholar
 

Nandi, D., Finck, A. D. K., Eisenstein, J. P., Pfeiffer, L. N. & West, K. W. Exciton condensation and perfect Coulomb drag. Nature 488, 481–484 (2012).

Article 

Google Scholar
 

Li, J. I. A., Taniguchi, T., Watanabe, K., Hone, J. & Dean, C. R. Excitonic superfluid phase in double bilayer graphene. Nat. Phys. 13, 751–755 (2017).

Article 

Google Scholar
 

Liu, X., Watanabe, K., Taniguchi, T., Halperin, B. I. & Kim, P. Quantum Hall drag of exciton condensate in graphene. Nat. Phys. 13, 746–750 (2017).

Article 

Google Scholar
 

Du, L. et al. Evidence for a topological excitonic insulator in InAs/GaSb bilayers. Nat. Commun. 8, 1971 (2017).

Article 

Google Scholar
 

Wang, R. et al. Excitonic topological order in imbalanced electron–hole bilayers. Nature 619, 57–62 (2023).

Article 

Google Scholar
 

Jia, Y. et al. Evidence for a monolayer excitonic insulator. Nat. Phys. 18, 87–93 (2022).

Article 

Google Scholar
 

Sun, B. et al. Evidence for equilibrium exciton condensation in monolayer WTe2. Nat. Phys. 18, 94–99 (2022).

Article 

Google Scholar
 

Ali, M. et al. Large, non-saturating magnetoresistance in WTe2. Nature 514, 205–208 (2014).

Article 

Google Scholar
 

Soluyanov, A. et al. Type-II Weyl semimetals. Nature 527, 495–498 (2015).

Article 

Google Scholar
 

Ma, X. et al. Ta2NiSe5: a candidate topological excitonic insulator with multiple band inversions. Phys. Rev. B 105, 035138 (2022).

Article 

Google Scholar
 

Wang, X. et al. Observation of topological edge states in the quantum spin Hall insulator Ta2Pd3Te5. Phys. Rev. B 104, L241408 (2021).

Article 

Google Scholar
 

Wang, A. et al. A robust and tunable Luttinger liquid in correlated edge of transition-metal second-order topological insulator Ta2Pd3Te5. Nat. Commun. 14, 7647 (2023).

Article 

Google Scholar
 

Fukutani, K. et al. Detecting photoelectrons from spontaneously formed excitons. Nat. Phys. 17, 1024–1030 (2021).

Article 

Google Scholar
 

Zhang, P. et al. Spontaneous gap opening and potential excitonic states in an ideal Dirac semimetal Ta2Pd3Te5. Phys. Rev. X 14, 011047 (2024).


Google Scholar
 

Huang, J. et al. Evidence for an excitonic insulator state in Ta2Pd3Te5. Phys. Rev. X 14, 011046 (2024).


Google Scholar
 

Yin, J.-X., Pan, S. H. & Hasan, M. Z. Probing topological quantum matter with scanning tunnelling microscopy. Nat. Rev. Phys. 3, 249 (2021).

Article 

Google Scholar
 

Yang, F. et al. Spatial and energy distribution of topological edge states in single Bi(111) bilayer. Phys. Rev. Lett. 109, 016801 (2012).

Article 

Google Scholar
 

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

Article 

Google Scholar
 

Pauly, C. et al. Subnanometre-wide electron channels protected by topology. Nat. Phys. 11, 338–343 (2015).

Article 

Google Scholar
 

Wu, R. et al. Evidence for topological edge states in a large energy gap near the step edges on the surface of ZrTe5. Phys. Rev. X 6, 021017 (2016).


Google Scholar
 

Li, X.-B. et al. Experimental observation of topological edge states at the surface step edge of the topological insulator ZrTe5. Phys. Rev. Lett. 116, 176803 (2016).

Article 

Google Scholar
 

Wang, Z. et al. Topological edge states in a high-temperature superconductor FeSe/SrTiO3(001) film. Nat. Mater. 15, 968–973 (2016).

Article 

Google Scholar
 

Sessi, P. et al. Robust spin-polarized midgap states at step edges of topological crystalline insulators. Science 354, 1269–1273 (2016).

Article 
MathSciNet 

Google Scholar
 

Peng, L. et al. Observation of topological states residing at step edges of WTe2. Nat. Commun. 8, 659 (2017).

Article 

Google Scholar
 

Liu, S. et al. Experimental observation of conductive edge states in weak topological insulator candidate HfTe5. APL Mater. 6, 121111 (2018).

Article 

Google Scholar
 

Ugeda, M. M. et al. Observation of topologically protected states at crystalline phase boundaries in single-layer WSe2. Nat. Commun. 9, 3401 (2018).

Article 

Google Scholar
 

Liu, R. Z. et al. Experimental observations indicating the topological nature of the edge states on HfTe5. Chin. Phys. Lett. 36, 117301 (2019).

Article 

Google Scholar
 

Shumiya, N. et al. Evidence of a room-temperature quantum spin Hall edge state in a higher-order topological insulator. Nat. Mater. 21, 1111–1115 (2022).

Article 

Google Scholar
 

Stühler, R. et al. Tomonaga–Luttinger liquid in the edge channels of a quantum spin Hall insulator. Nat. Phys. 16, 47–51 (2020).

Article 

Google Scholar
 

Shi, Y. et al. Imaging quantum spin Hall edges in monolayer WTe2. Sci. Adv. 5, eaat8799 (2019).

Article 

Google Scholar
 

Dominguez, F. et al. Testing topological protection of edge states in hexagonal quantum spin Hall candidate materials. Phys. Rev. B 98, 161407(R) (2018).

Article 

Google Scholar
 

Fu, Y. S. et al. Observation of Zeeman effect in topological surface state with distinct material dependence. Nat. Commun. 7, 10829 (2016).

Article 

Google Scholar
 

Qi, X.-L. & Zhang, S.-C. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057 (2011).

Article 

Google Scholar
 

Bernevig, B. A. & Hughes, T. L. Topological Insulators and Topological Superconductors (Princeton Univ. Press, 2013).

Chen, C., Singh, B., Lin, H. & Pereira, V. M. Reproduction of the charge density wave phase diagram in 1T−TiSe2 exposes its excitonic character. Phys. Rev. Lett. 121, 226602 (2018).

Article 

Google Scholar
 

Rachel, S. Interacting topological insulators: a review. Rep. Prog. Phys. 81, 116501 (2018).

Article 

Google Scholar
 

Hohenberg, P. & Kohn, W. Inhomogeneous electron gas. Phys. Rev. 136, B864 (1964).

Article 
MathSciNet 

Google Scholar
 

Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169 (1996).

Article 

Google Scholar
 

Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996).

Article 

Google Scholar
 

Mostofi, A. et al. Wannier90: a tool for obtaining maximally-localised Wannier functions. Comput. Phys. Commun. 178, 685 (2008).

Article 

Google Scholar
 

Wu, Q., Zhang, S., Song, H.-F., Troyer, M. & Soluyanov, A. A. WannierTools: an open-source software package for novel topological materials. Comput. Phys. Commun. 224, 405 (2018).

Article 

Google Scholar
 

Lee, I. et al. Imaging Dirac-mass disorder from magnetic dopant atoms in the ferromagnetic topological insulator Crx(Bi0.1Sb0.9)2−xTe3. Proc. Natl Acad. Sci. USA 112, 1316–1321 (2014).

Article 

Google Scholar
 

Edelstein, W. et al. Two-dimensional excitons in magnetic fields. Phys. Rev. B 39, 7697 (1989).

Article 

Google Scholar
 

Stier, A. et al. Exciton diamagnetic shifts and valley Zeeman effects in monolayer WS2 and MoS2 to 65 tesla. Nat. Commun. 7, 10643 (2016).

Article 

Google Scholar
 

Grüner, G. The dynamics of charge-density waves. Rev. Mod. Phys. 60, 1129–1181 (1988).

Article 

Google Scholar
 

Bernevig, B. A., Hughes, T. L. & Shou-Cheng Zhang, S.-C. Quantum spin Hall effect and topological phase transition in HgTe quantum wells. Science 314, 1757–1761 (2006).

Article 

Google Scholar
 

Gao, Q. et al. Evidence of high-temperature exciton condensation in a two-dimensional semimetal. Nat. Commun. 14, 994 (2023).

Article 

Google Scholar
 

Cudazzo, P., Tokatly, I. V. & Rubio, A. Dielectric screening in two-dimensional insulators: implications for excitonic and impurity states in graphene. Phys. Rev. B 84, 085406 (2011).

Article 

Google Scholar
 

Varsano, D., Palummo, M., Molinari, E. & Rontani, M. A monolayer transition-metal dichalcogenide as a topological excitonic insulator. Nat. Nanotechnol. 15, 367 (2020).

Article 

Google Scholar
 

Amaricci, A., Mazza, G., Capone, M. & Fabrizio, M. Exciton condensation in strongly correlated quantum spin Hall insulators. Phys. Rev. B 107, 115117 (2023).

Article 

Google Scholar
 

Blason, A. & Fabrizio, M. Exciton topology and condensation in a model quantum spin Hall insulator. Phys. Rev. B 102, 035146 (2020).

Article 

Google Scholar
 

Cong, K., Noe, G. T. & Kono, J. in Encyclopedia of Modern Optics 2nd edn (eds Guenther, B. D. & Steel, D.) 63–81 (Elsevier, 2018).

Jahan, K. L. et al. Magnetic field effect on the energy levels of an exciton in a GaAs quantum dot: application for excitonic lasers. Sci. Rep. 8, 5073 (2018).

Article 

Google Scholar
 

Förste, J. et al. Exciton g-factors in monolayer and bilayer WSe2 from experiment and theory. Nat. Commun. 11, 4539 (2020).

Article 

Google Scholar
 

Fenton, E. W. Excitonic insulator in a magnetic field. Phys. Rev. 170, 816 (1968).

Article 

Google Scholar