[1]

Haldane FDM, Raghu S. Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry. Phys Rev Lett 2008;100:013904. CrossrefPubMedGoogle Scholar

[2]

Raghu S, Haldane FDM. Analogs of quantum-Hall-effect edge states in photonic crystals. Phys Rev A 2008;78:033834. CrossrefGoogle Scholar

[3]

Wang Z, Chong Y, Joannopoulos JD, Soljačić M. Observation of unidirectional backscattering-immune topological electromagnetic states. Nature 2009;461:772–5. CrossrefPubMedGoogle Scholar

[4]

Rechtsman MC, Zeuner JM, Plotnik Y, et al. Photonic Floquet topological insulators. Nature 2013;496:196–200. PubMedCrossrefGoogle Scholar

[5]

Hafezi M, Demler EA, Lukin MD, Taylor JM. Robust optical delay lines with topological protection. Nat Phys 2011;7:907–12. CrossrefGoogle Scholar

[6]

Hafezi M, Mittal S, Fan J, Migdall A, Taylor JM. Imaging topological edge states in silicon photonics. Nat Photonics 2013;7:1001–5. CrossrefGoogle Scholar

[7]

Khanikaev AB, Mousavi SH, Tse W-K, Kargarian M, MacDonald AH, Shvets G. Photonic topological insulators. Nat Mater 2013;12:233–9. CrossrefPubMedGoogle Scholar

[8]

Chen W-J, Jiang S-J, Chen X-D, et al. Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide. Nat Commun 2014;5:5782. CrossrefGoogle Scholar

[9]

Wu L-H, Hu X. Scheme for achieving a topological photonic crystal by using dielectric material. Phys Rev Lett 2015;114:223901. CrossrefPubMedGoogle Scholar

[10]

Yves S, Fleury R, Berthelot T, Fink M, Lemoult F, Lerosey G.Crystalline metamaterials for topological properties at subwavelength scales. Nat Commun 2017;8:16023. PubMedCrossrefGoogle Scholar

[11]

Barik S, Karasahin A, Flower C, et al. A topological quantum optics interface. Science 2018;359:666–8. PubMedCrossrefGoogle Scholar

[12]

Yang Y, Xu YF, Xu T, et al. Visualization of a unidirectional electromagnetic waveguide using topological photonic crystals made of dielectric materials. Phys Rev Lett 2018;120:217401. CrossrefPubMedGoogle Scholar

[13]

Ma T, Shvets G. All-Si valley-Hall photonic topological insulator. New J Phys 2016;18:025012. CrossrefGoogle Scholar

[14]

Gao F, Xue H, Yang Z, et al. Topologically protected refraction of robust kink states in valley photonic crystals. Nat Phys 2018;14:140–4. CrossrefGoogle Scholar

[15]

Noh J, Huang S, Chen KP, Rechtsman MC. Observation of photonic topological valley hall edge states. Phys Rev Lett 2018;120:63902. CrossrefGoogle Scholar

[16]

Lu L, Joannopoulos JD, Soljačić M. Topological photonics. Nat Photonics 2014;8:821–9. CrossrefGoogle Scholar

[17]

Lu L, Joannopoulos JD, Soljačić M. Topological states in photonic systems. Nat Phys 2016;12:626–9. CrossrefGoogle Scholar

[18]

Khanikaev AB, Shvets G. Two-dimensional topological photonics. Nat Photonics 2017;11:763–73. CrossrefGoogle Scholar

[19]

Sun XC, He C, Liu XP, Lu MH, Zhu SN, Chen YF. Two-dimensional topological photonic systems. Prog Quantum Electron 2017;55:52–73. CrossrefGoogle Scholar

[20]

Wu Y, Li C, Hu X, Ao Y, Zhao Y, Gong Q. Applications of topological photonics in integrated photonic devices. Adv Opt Mater 2017;5:1700357. CrossrefGoogle Scholar

[21]

Ozawa T, Price HM, Amo A. Topological photonics. Rev Mod Phys 2019;91:015006. CrossrefGoogle Scholar

[22]

Rider MS, Palmer SJ, Pocock SR, Xiao X, Arroyo Huidobro P, Giannini V. A perspective on topological nanophotonics: current status and future challenges. J Appl Phys 2019;125:120901. CrossrefGoogle Scholar

[23]

Simanova D, Leykam D, Chong Y, Kishvar Y. Nonlinear topological photonics. arXiv:1912.01784. https://arxiv.org/abs/1912.01784.

[24]

Foa Torres LEF. Perspective on topological states of non-Hermitian systems. J Phys Mater 2020;3:014002. Google Scholar

[25]

Parto M, Wittek S, Hodaei H, et al. Edge-mode lasing in 1D topological active arrays. Phys Rev Lett 2018;120:113901. CrossrefPubMedGoogle Scholar

[26]

St-Jean P, Goblot V, Galopin E, et al. Lasing in topological edge states of a one-dimensional lattice. Nat Photonics 2017;11:651–6. CrossrefGoogle Scholar

[27]

Zhao H, Miao P, Teimourpour MH, et al. Topological hybrid silicon microlasers. Nat Commun 2018;9:981. PubMedCrossrefGoogle Scholar

[28]

Han C, Lee M, Callard S, Seassal C, Jeon H. Lasing at topological edge states in a photonic crystal L3 nanocavity dimer array. Light Sci Appl 2019;8:40. CrossrefGoogle Scholar

[29]

Ota Y, Katsumi R, Watanabe K, Iwamoto S, Arakawa Y.Topological photonic crystal nanocavity laser. Commun Phys 2018;1:86. CrossrefGoogle Scholar

[30]

Bahari B, Ndao A, Vallini F, El Amili A, Fainman Y, Kanté B. Nonreciprocal lasing in topological cavities of arbitrary geometries. Science 2017;358:636–40. PubMedCrossrefGoogle Scholar

[31]

Bandres MA, Wittek S, Harari G, et al. Topological insulator laser: experiments. Science 2018;359:4005. CrossrefGoogle Scholar

[32]

Klembt S, Harder TH, Egorov OA, et al. Exciton-polariton topological insulator. Nature 2018;562:552–6. PubMedCrossrefGoogle Scholar

[33]

Miao P, Zhang Z, Sun J, et al. Orbital angular momentum microlaser. Science 2016;353:464–7. CrossrefPubMedGoogle Scholar

[34]

Carlon Zambon N, St-Jean P, Milićević M, et al. Optically controlling the emission chirality of microlasers. Nat Photonics 2019;13:283–8. CrossrefGoogle Scholar

[35]

Bahari B, Hsu L-Y, Pan SH, et al. Topological lasers generating and multiplexing topological light. 2019. arXiv: 1904.11873. https://arxiv.org/abs/1904.11873.

[36]

Söllner I, Mahmoodian S, Hansen SL, et al. Deterministic photon–emitter coupling in chiral photonic circuits. Nat Nanotechnol 2015;10:775–8. CrossrefPubMedGoogle Scholar

[37]

Blanco-Redondo A, Bell B, Oren D, Eggleton BJ, Segev M. Topological protection of biphoton states. Science 2018;362:568–71. CrossrefPubMedGoogle Scholar

[38]

Mittal S, Goldschmidt EA, Hafezi M. A topological source of quantum light. Nature 2018;561:502–6. PubMedCrossrefGoogle Scholar

[39]

Fang K, Yu Z, Fan S. Realizing effective magnetic field for photons by controlling the phase of dynamic modulation. Nat Photonics 2012;6:782–7. CrossrefGoogle Scholar

[40]

Yuan L, Lin Q, Xiao M, Fan S. Synthetic dimension in photonics. Optica 2018;5:1396–405. CrossrefGoogle Scholar

[41]

Ozawa T, Price HM. Topological quantum matter in synthetic dimensions. Nat Rev Phys 2019;1:349–57. CrossrefGoogle Scholar

[42]

Asbóth JK, Oroszlány L, Pályi A. A short course on topological insulators, lecture notes in physics, Vol. 919. Cham, Switzerland, Springer International Publishing, 2016. Google Scholar

[43]

Delplace P, Ullmo D, Montambaux G. Zak phase and the existence of edge states in graphene. Phys Rev B 2011;84:195452. CrossrefGoogle Scholar

[44]

Zeuner JM, Rechtsman MC, Plotnik Y, et al. Observation of a topological transition in the bulk of a non-hermitian system. Phys Rev Lett 2015;115:040402. PubMedCrossrefGoogle Scholar

[45]

Blanco-Redondo A, Andonegui I, Collins MJ, et al. Topological optical waveguiding in silicon and the transition between topological and trivial defect states. Phys Rev Lett 2016;116:163901. PubMedCrossrefGoogle Scholar

[46]

Poli C, Bellec M, Kuhl U, Mortessagne F, Schomerus H. Selective enhancement of topologically induced interface states in a dielectric resonator chain. Nat Commun 2015;6:6710. CrossrefGoogle Scholar

[47]

Sinev IS, Mukhin IS, Slobozhanyuk AP, et al. Mapping plasmonic topological states at the nanoscale. Nanoscale 2015;7:11904–8. CrossrefPubMedGoogle Scholar

[48]

Kruk S, Slobozhanyuk A, Denkova D, et al. Edge states and topological phase transitions in chains of dielectric nanoparticles. Small 2017;13:1603190. CrossrefGoogle Scholar

[49]

Schomerus H. Topologically protected midgap states in complex photonic lattices. Opt Lett 2013;38:1912–4. CrossrefPubMedGoogle Scholar

[50]

Malzard S, Schomerus H. Nonlinear mode competition and symmetry-protected power oscillations in topological lasers. New J Phys 2018;20:063044. CrossrefGoogle Scholar

[51]

Poddubny A, Miroshnichenko A, Slobozhanyuk A, Kivshar Y. Topological majorana states in zigzag chains of plasmonic nanoparticles. ACS Photonics 2014;1:101–5. CrossrefGoogle Scholar

[52]

Pilozzi L, Conti C. Topological lasing in resonant photonic structures. Phys Rev B 2016;93:195317. CrossrefGoogle Scholar

[53]

Alpeggiani F, Andreani LC, Gerace D. Effective bichromatic potential for ultra-high Q-factor photonic crystal slab cavities. Appl Phys Lett 2015;107:261110. CrossrefGoogle Scholar

[54]

Simbula A, Schatzl M, Zagaglia L. Realization of high- Q/V photonic crystal cavities defined by an effective Aubry-André-Harper bichromatic potential. APL Photonics 2017;2:056102. CrossrefGoogle Scholar

[55]

Alpeggiani F, Kuipers L. Topological edge states in bichromatic photonic crystals. Optica 2019;6:96–103. CrossrefGoogle Scholar

[56]

Benalcazar WA, Bernevig BA, Hughes TL. Quantized electric multipole insulators. Science 2017;357:61–6. CrossrefPubMedGoogle Scholar

[57]

Benalcazar WA, Bernevig BA, Hughes TL. Electric multipole moments, topological multipole moment pumping, and chiral hinge states in crystalline insulators. Phys Rev B 2017;96:245115. CrossrefGoogle Scholar

[58]

Peterson CW, Benalcazar WA, Hughes TL, Bahl G. A quantized microwave quadrupole insulator with topologically protected corner states. Nature 2018;555:346–50. CrossrefPubMedGoogle Scholar

[59]

Xie B-Y, Wang H-F, Wang H-X, et al. Second-order photonic topological insulator with corner states. Phys Rev B 2018;98:205147. CrossrefGoogle Scholar

[60]

Noh J, Benalcazar WA, Huang S, et al. Topological protection of photonic mid-gap defect modes. Nat Photonics 2018;12:408–15. CrossrefGoogle Scholar

[61]

Xie B, Su G, Wang H, Su H, Shen X, Zhan P. Visualization of higher-order topological insulating phases in two-dimensional dielectric photonic crystals. Phys Rev Lett 2019;122:233903. PubMedCrossrefGoogle Scholar

[62]

El Hassan A, Kunst FK, Moritz A, Andler G, Bergholtz EJ, Bourennane M. Corner states of light in photonic waveguides. Nat Photonics 2019;13:697–700. CrossrefGoogle Scholar

[63]

Mittal S, Orre VV, Zhu G, Gorlach MA, Poddubny A, Hafezi M. Photonic quadrupole topological phases. Nat Photonics 2019;13:692–6. CrossrefGoogle Scholar

[64]

Chen XD, Deng WM, Shi FL, Zhao FL, Chen M, Dong JW. Direct observation of corner states in second-order topological photonic crystal slabs. Phys Rev Lett 2019;122:233902. CrossrefPubMedGoogle Scholar

[65]

Ota Y, Liu F, Katsumi R, et al. Photonic crystal nanocavity based on a topological corner state. Optica 2019;6:786–9. CrossrefGoogle Scholar

[66]

Ji C-Y, Liu G-B, Zhang Y, Zou B, Yao Y. Transport tuning of photonic topological edge states by optical cavities. Phys Rev A 2019;99:043801. CrossrefGoogle Scholar

[67]

Li F-F, Wang H-X, Xiong Z, et al. Topological light-trapping on a dislocation. Nat Commun 2018;9:2462. CrossrefPubMedGoogle Scholar

[68]

Xiao M, Zhang ZQ, Chan CT. Surface impedance and bulk band geometric phases in one-dimensional systems. Phys Rev X 2014;4:021017. Google Scholar

[69]

Kalozoumis PA, Theocharis G, Achilleos V, Félix S, Richoux O, Pagneux V. Finite-size effects on topological interface states in one-dimensional scattering systems. Phys Rev A 2018;98:023838. CrossrefGoogle Scholar

[70]

Liu F, Deng H, Wakabayashi K. Topological photonic crystals with zero Berry curvature. Phys Rev B 2018;97:035442. CrossrefGoogle Scholar

[71]

Gorlach AA, Zhirihin DV, Slobozhanyuk AP, Khanikaev AB,Gorlach MA. Photonic Jackiw-Rebbi states in all-dielectric structures controlled by bianisotropy. Phys Rev B 2019;99:205122. CrossrefGoogle Scholar

[72]

Wang Z, Chong YD, Joannopoulos JD, Soljačić M. Reflection-free one-way edge modes in a gyromagnetic photonic crystal. Phys Rev Lett 2008;100:013905. CrossrefGoogle Scholar

[73]

Harari G, Bandres MA, Lumer Y, et al. Topological insulator laser: theory. Science 2018;359:eaar4003. PubMedCrossrefGoogle Scholar

[74]

Kavokin A, Malpuech G, Glazov M. Optical spin hall effect. Phys Rev Lett 2005;95:136601. PubMedCrossrefGoogle Scholar

[75]

Sala VG, Solnyshkov DD, Carusotto I, et al. Spin-Orbit coupling for photons and polaritons in microstructures. Phys Rev X 2015;5:011034. Google Scholar

[76]

Nalitov AV, Solnyshkov DD, Malpuech G. Polariton Z topological insulator. Phys Rev Lett 2015;114:116401. CrossrefGoogle Scholar

[77]

Kartashov YV, Skryabin DV. Two-dimensional topological polariton laser. Phys Rev Lett 2019;122:083902. PubMedCrossrefGoogle Scholar

[78]

Karzig T, Bardyn C-E, Lindner NH, Refael G. Topological polaritons. Phys Rev X 2015;5:031001. Google Scholar

[79]

Schneider C, Rahimi-Iman A, Kim NY, et al. An electrically pumped polariton laser. Nature 2013;497:348–52. PubMedCrossrefGoogle Scholar

[80]

Carusotto I, Ciuti C. Quantum fluids of light. Rev Mod Phys 2013;85:299–366. CrossrefGoogle Scholar

[81]

Kartashov YV, Skryabin DV. Modulational instability and solitary waves in polariton topological insulators. Optica 2016;3:1228–36. CrossrefGoogle Scholar

[82]

Kartashov YV, Skryabin DV. Bistable topological insulator with exciton-polaritons. Phys Rev Lett 2017;119:253904. PubMedCrossrefGoogle Scholar

[83]

Kane CL, Mele EJ. Z2 topological order and the quantum spin hall effect. Phys Rev Lett 2005;95:146802. CrossrefPubMedGoogle Scholar

[84]

Kane CL, Mele EJ. Quantum spin hall effect in graphene. Phys Rev Lett 2005;95:226801. PubMedCrossrefGoogle Scholar

[85]

Bernevig BA, Hughes TL, Zhang S-C. Quantum spin hall effect and topological phase transition in HgTe quantum wells. Science 2006;314:1757–61. CrossrefPubMedGoogle Scholar

[86]

Schnyder AP, Ryu S, Furusaki A, Ludwig AWW. Classification of topological insulators and superconductors in three spatial dimensions. Phys Rev B 2008;78:195125. CrossrefGoogle Scholar

[87]

Kitaev A, Lebedev V, Feigel’man M. Periodic table for topological insulators and superconductors. In AIP Conference Proceedings (AIP, 2009), pp. 22–30. Google Scholar

[88]

Seclì M, Capone M, Carusotto I. Theory of chiral edge state lasing in a two-dimensional topological system. 2019. arXiv: 1901.01290. https://arxiv.org/abs/1901.01290.

[89]

Seclì M. Edge state lasing in a 2D topological photonic system. Master thesis. Trento, Italy, University of Trento, 2017. Google Scholar

[90]

Moiseyev N. Non-Hermitian quantum mechanics. Cambridge, UK, Cambridge University Press, 2011. https://doi.org/10.1017/CBO9780511976186.

[91]

Bender CM, Boettcher S. Real spectra in non-hermitian hamiltonians having PT symmetry. Phys Rev Lett 1998;80:5243–6. CrossrefGoogle Scholar

[92]

Makris KG, El-Ganainy R, Christodoulides DN, Musslimani ZH. Beam dynamics in PT symmetric optical lattices. Phys Rev Lett 2008;100:103904. PubMedCrossrefGoogle Scholar

[93]

Feng L, El-Ganainy R, Ge L. Non-Hermitian photonics based on parity–time symmetry. Nat Photonics 2017;11:752–62. CrossrefGoogle Scholar

[94]

El-Ganainy R, Makris KG, Khajavikhan M, Musslimani ZH, Rotter S, Christodoulides DN. Non-Hermitian physics and PT symmetry. Nat Phys 2018;14:11–9. CrossrefGoogle Scholar

[95]

Özdemir K, Rotter S, Nori F, Yang L. Parity–time symmetry and exceptional points in photonics. Nat Mater 2019;18:783–98. CrossrefPubMedGoogle Scholar

[96]

Su WP, Schrieffer JR, Heeger AJ. Solitons in polyacetylene. Phys Rev Lett 1979;42:1698–701. CrossrefGoogle Scholar

[97]

Klett M, Cartarius H, Dast D, Main J, Wunner G. Relation between PT -symmetry breaking and topologically nontrivial phases in the Su-Schrieffer-Heeger and Kitaev models. Phys Rev A 2017;95:053626. CrossrefGoogle Scholar

[98]

Yuce C. Edge states at the interface of non-Hermitian systems. Phys Rev A 2018;97:042118. CrossrefGoogle Scholar

[99]

Zak J. Berrys phase for energy bands in solids. Phys Rev Lett 1989;62:2747–50. CrossrefGoogle Scholar

[100]

Rudner MS, Levitov LS. Topological transition in a non-hermitian quantum walk. Phys Rev Lett 2009;102:065703. CrossrefGoogle Scholar

[101]

Yin C, Jiang H, Li L, Lü R, Chen S. Geometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral non-Hermitian systems. Phys Rev A 2018;97:052115. CrossrefGoogle Scholar

[102]

Weimann S, Kremer M, Plotnik Y, et al. Topologically protected bound states in photonic parity–time-symmetric crystals. Nat Mater 2017;16:433–8. CrossrefPubMedGoogle Scholar

[103]

Song W, Sun W, Chen C, et al. Breakup and recovery of topological zero modes in finite non-Hermitian optical lattices. Phys Rev Lett 2019;123:165701. CrossrefPubMedGoogle Scholar

[104]

Takata K, Notomi M. Photonic topological insulating phase induced solely by gain and loss. Phys Rev Lett 2018;121:213902. CrossrefPubMedGoogle Scholar

[105]

Guo A, Salamo GJ, Duchesne D, et al. Observation of PT-symmetry breaking in complex optical potentials. Phys Rev Lett 2009;103:93902. CrossrefGoogle Scholar

[106]

Liang SD, Huang GY. Topological invariance and global Berry phase in non-Hermitian systems. Phys Rev A: At Mol Opt Phys 2013;87:012118. CrossrefGoogle Scholar

[107]

Esaki K, Sato M, Hasebe K, Kohmoto M. Edge states and topological phases in non-Hermitian systems. Phys Rev B: Condens Matter Mater Phys 2011;84:205128. CrossrefGoogle Scholar

[108]

Sato M, Hasebe K, Esaki K, Kohmoto M. Time-reversal symmetry in non-Hermitian systems. Prog Theor Phys 2012;127:937–74. CrossrefGoogle Scholar

[109]

Feng L, Wong ZJ, Ma R-M, Wang Y, Zhang X. Single-mode laser by parity-time symmetry breaking. Science 2014;80:972–5. Google Scholar

[110]

Takata K, Notomi M. PT-Symmetric coupled-resonator waveguide based on buried heterostructure nanocavities. Phys Rev Appl 2017;7:054023. CrossrefGoogle Scholar

[111]

Zhou L, Wang QH, Wang H, Gong J. Dynamical quantum phase transitions in non-Hermitian lattices. Phys Rev A 2018;98:022129. CrossrefGoogle Scholar

[112]

Malzard S, Cancellieri E, Schomerus H. Topological dynamics and excitations in lasers and condensates with saturable gain or loss. Opt Express 2018;26:22506. CrossrefPubMedGoogle Scholar

[113]

Luo X-W, Zhang C. Higher-order topological corner states induced by gain and loss. Phys Rev Lett 2019;123:073601. CrossrefPubMedGoogle Scholar

[114]

Leykam D, Bliokh KY, Huang C, Chong YD, Nori F. Edge modes, degeneracies, and topological numbers in non-Hermitian systems. Phys Rev Lett 2017;118:28–30. Google Scholar

[115]

Shen H, Zhen B, Fu L. Topological band theory for non-Hermitian Hamiltonians. Phys Rev Lett 2018;120:146402. PubMedCrossrefGoogle Scholar

[116]

Malzard S, Schomerus H. Bulk and edge-state arcs in non-Hermitian coupled-resonator arrays. Phys Rev A 2018;98:033807. CrossrefGoogle Scholar

[117]

Kawabata K, Shiozaki K, Ueda M. Anomalous helical edge states in a non-Hermitian Chern insulator. Phys Rev B 2018;98:165148. CrossrefGoogle Scholar

[118]

Kawabata K, Higashikawa S, Gong Z, Ashida Y, Ueda M. Topological unification of time-reversal and particle-hole symmetries in non-Hermitian physics. Nat Commun 2019;10:297. CrossrefPubMedGoogle Scholar

[119]

Carlström J, Bergholtz EJ. Exceptional links and twisted Fermi ribbons in non-Hermitian systems. Phys Rev A 2018;98:042114. CrossrefGoogle Scholar

[120]

Zhou H, Lee JY, Liu S, Zhen B. Exceptional surfaces in PT-symmetric non-Hermitian photonic systems. Optica 2019;6:190. CrossrefGoogle Scholar

[121]

Wang H, Ruan J, Zhang H. Non-Hermitian nodal-line semimetals with an anomalous bulk-boundary correspondence. Phys Rev B 2019;99:075130. CrossrefGoogle Scholar

[122]

Yang Z, Hu J. Non-Hermitian Hopf-link exceptional line semimetals. Phys Rev B 2019;99:081102. CrossrefGoogle Scholar

[123]

Arkinstall J, Teimourpour MH, Feng L, El-Ganainy R, Schomerus H. Topological tight-binding models from nontrivial square roots. Phys Rev B 2017;95:165109. CrossrefGoogle Scholar

[124]

Lieu S. Topological symmetry classes for non-Hermitian models and connections to the bosonic Bogoliubov-de Gennes equation. Phys Rev B 2018;98:115135. CrossrefGoogle Scholar

[125]

Kawabata K, Shiozaki K, Ueda M, Sato M. Symmetry and topology in non-Hermitian physics. Phys Rev X 2019;9:041015. Google Scholar

[126]

Zhou H, Lee JY. Periodic table for topological bands with non-Hermitian symmetries. Phys Rev B 2019;99:235112. CrossrefGoogle Scholar

[127]

Altland A, Zirnbauer MR. Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures. Phys Rev B 1997;55:1142–61. CrossrefGoogle Scholar

[128]

Ryu S, Schnyder AP, Furusaki A, Ludwig AWW. Topological insulators and superconductors: tenfold way and dimensional hierarchy. New J Phys 2010;12:065010. CrossrefGoogle Scholar

[129]

Hasan MZ, Kane CL. Colloquium: topological insulators. Rev Mod Phys 2010;82:3045–67. CrossrefGoogle Scholar

[130]

Qi X-L, Zhang S-C. Topological insulators and superconductors. Rev Mod Phys 2011;83:1057–110. CrossrefGoogle Scholar

[131]

Gong Z, Ashida Y, Kawabata K, Takasan K, Higashikawa S, Ueda M. Topological phases of non-Hermitian systems. Phys Rev X 2018;8:031079. Google Scholar

[132]

Longhi S, Gatti D, Della Valle G. Robust light transport in non-Hermitian photonic lattices. Sci Rep 2015;5:13376. CrossrefPubMedGoogle Scholar

[133]

Longhi S, Gatti D, Della Valle G. Non-Hermitian transparency and one-way transport in low-dimensional lattices by an imaginary gauge field. Phys Rev B 2015;92:094204. CrossrefGoogle Scholar

[134]

Lee TE. Anomalous edge state in a non-Hermitian lattice. Phys Rev Lett 2016;116:133903. CrossrefGoogle Scholar

[135]

Herviou L, Bardarson JH, Regnault N. Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition. Phys Rev A 2019;99:052118. CrossrefGoogle Scholar

[136]

Ghatak A, Das T. New topological invariants in non-Hermitian systems. J Phys Condens Matter 2019;31:263001. CrossrefPubMedGoogle Scholar

[137]

Yokomizo K, Murakami S. Non-Bloch band theory of non-Hermitian systems. Phys Rev Lett 2019;123:066404. PubMedCrossrefGoogle Scholar

[138]

Yao S, Song F, Wang Z. Non-Hermitian Chern bands. Phys Rev Lett 2018;121:136802. PubMedCrossrefGoogle Scholar

[139]

Yao S, Wang Z. Edge states and topological invariants of non-Hermitian systems. Phys Rev Lett 2018;121:086803. CrossrefPubMedGoogle Scholar

[140]

Kunst FK, Edvardsson E, Budich JC, Bergholtz EJ. Biorthogonal bulk-boundary correspondence in non-Hermitian systems. Phys Rev Lett 2018;121:026808. CrossrefPubMedGoogle Scholar

[141]

Martinez Alvarez VM, Barrios Vargas JE, Foa Torres LEF. Non-Hermitian robust edge states in one dimension: anomalous localization and eigenspace condensation at exceptional points. Phys Rev B 2018;97:121401. CrossrefGoogle Scholar

[142]

Jin L, Song Z. Bulk-boundary correspondence in a non-Hermitian system in one dimension with chiral inversion symmetry. Phys Rev B 2019;99:081103. CrossrefGoogle Scholar

[143]

Wang P, Jin L, Song Z. Non-Hermitian phase transition and eigenstate localization induced by asymmetric coupling. Phys Rev A 2019;99:062112. CrossrefGoogle Scholar

[144]

Ozcakmakli Turker Z, Yuce C. Open and closed boundaries in non-Hermitian topological systems. Phys Rev A 2019;99:022127. CrossrefGoogle Scholar

[145]

Lee CH, Thomale R. Anatomy of skin modes and topology in non-Hermitian systems. Phys Rev B 2019;99:201103. CrossrefGoogle Scholar

[146]

Hatano N, Nelson DR. Localization transitions in non-hermitian quantum mechanics. Phys Rev Lett 1996;77:570–3. PubMedCrossrefGoogle Scholar

[147]

Ge Z-Y, Zhang Y-R, Liu T, Li S-W, Fan H, Nori F. Topological band theory for non-Hermitian systems from the Dirac equation. Phys Rev B 2019;100:054105. CrossrefGoogle Scholar

[148]

Okuma N, Kawabata K, Shiozaki K, Sato M. Topological origin of non-Hermitian skin effects. 2019. arXiv: 1910.02878. https://arxiv.org/abs/1910.02878.

[149]

Heiss WD. Repulsion of resonance states and exceptional points. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Top 2000;61:929–32. Google Scholar

[150]

Heiss WD. The physics of exceptional points. J Phys A Math Theor 2012;45:444016. CrossrefGoogle Scholar

[151]

Dembowski C, Gräf HD, Harney HL, et al. Experimental observation of the topological structure of exceptional points. Phys Rev Lett 2001;86:787–90. PubMedCrossrefGoogle Scholar

[152]

Zhen B, Hsu CW, Igarashi Y, et al. Spawning rings of exceptional points out of Dirac cones. Nature 2015;525:354–8. PubMedCrossrefGoogle Scholar

[153]

Hodaei H, Hassan AU, Wittek S. Enhanced sensitivity at higher-order exceptional points. Nature 2017;548:187–91. CrossrefPubMedGoogle Scholar

[154]

Chen W, Kaya Özdemir Ş, Zhao G, Wiersig J, Yang L. Exceptional points enhance sensing in an optical microcavity. Nature 2017;548:192–6. CrossrefGoogle Scholar

[155]

Assawaworrarit S, Yu X, Fan S. Robust wireless power transfer using a nonlinear parity-time-symmetric circuit. Nature 2017;546:387–90. PubMedCrossrefGoogle Scholar

[156]

Kawabata K, Bessho T, Sato M. Classification of exceptional points and non-Hermitian topological semimetals. Phys Rev Lett 2019;123:066405. PubMedCrossrefGoogle Scholar

[157]

Lin S, Jin L, Song Z. Symmetry protected topological phases characterized by isolated exceptional points. Phys Rev B 2019;99:165148. CrossrefGoogle Scholar

[158]

Yuce C. Topological states at exceptional points. Phys Lett Sect A Gen At Solid State Phys 2019;383:2567–70. Google Scholar

[159]

Yoshida T, Hatsugai Y. Exceptional rings protected by emergent symmetry for mechanical systems. Phys Rev B 2019;100:054109. CrossrefGoogle Scholar

[160]

Malzard S, Poli C, Schomerus H. Topologically protected defect states in open photonic systems with non-Hermitian charge-conjugation and parity-time symmetry. Phys Rev Lett 2015;115:200402. PubMedCrossrefGoogle Scholar

[161]

Zhao H, Longhi S, Feng L. Robust light state by quantum phase transition in non-Hermitian optical materials. Sci Rep 2015;5:17022. CrossrefPubMedGoogle Scholar

[162]

Pan M, Zhao H, Miao P, Longhi S, Feng L. Photonic zero mode in a non-Hermitian photonic lattice. Nat Commun 2018;9:1308. CrossrefGoogle Scholar

[163]

Zhou H, Peng C, Yoon Y, et al. Observation of bulk Fermi arc and polarization half charge from paired exceptional points. Science 2018;359:1009–12. CrossrefPubMedGoogle Scholar

[164]

Zhao H, Qiao X, Wu T, Midya B, Longhi S, Feng L.Non-Hermitian topological light steering. Science 2019;365:1163–6. CrossrefPubMedGoogle Scholar

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