Haldane, FDM Nobel Lecture: Topological quantum matter. Rev. mod. Phys. 89040502 (2017).
Kosterlitz, JM Nobel Lecture: Topological defects and phase transitions. Rev. Mod. Phys. 89040501 (2017).
Yao, S. & Wang, Z. Edge states and topological invariants of non-Hermitian systems. Phys. Rev. Lett. 121086803 (2018).
McDonald, A., Pereg-Barnea, T. & Clerk, AA Phase-dependent chiral transport and effective non-Hermitian dynamics in a bosonic Kitaev-Majorana chain. Phys. Rev. X 8041031 (2018).
Google Scholar
Kunst, FK, Edvardsson, E., Budich, JC & Bergholtz, EJ Biorthogonal bulk-boundary correspondence in non-Hermitian systems. Phys. Rev. Lett. 121026808 (2018).
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 97121401 (2018).
Ozawa, T. et al. Topological photonics. Rev. mod. Phys. 91015006 (2019).
Ma, G., Xiao, M. & Chan, CT Topological phases in acoustic and mechanical systems. Nat. Rev. Phys. 1281–294 (2019).
Hafezi, M., Demler, EA, Lukin, MD & Taylor, JM Robust optical delay lines with topological protection. Nat. Phys. 7907–912 (2011).
Xu, C., Chen, Z.-G., Zhang, G., Ma, G. & Wu, Y. Multi-dimensional wave steering with higher-order topological phononic crystal. Science. Bull. 661740–1745 (2021).
Hu, B. et al. Non-Hermitian topological whispering gallery. Nature 597655–659 (2021).
St-Jean, P. et al. Lasing in topological edge states of a one-dimensional lattice. Nat. Photonics 11651–656 (2017).
Harari, G. et al. Topological insulator laser: theory. Science 359eaar4003 (2018).
Bandres, MA et al. Topological insulator laser: experiments. Science 359eaar4005 (2018).
Zeng, Y. et al. Electrically pumped topological laser with valley edge modes. Nature 578246–250 (2020).
Barik, S. et al. A topological quantum optics interface. Science 359666–668 (2018).
Blanco-Redondo, A., Bell, B., Oren, D., Eggleton, BJ & Segev, M. Topological protection of biphoton states. Science 362568–571 (2018).
Mittal, S., Goldschmidt, EA & Hafezi, M. A topological source of quantum light. Nature 561502–506 (2018).
Bender, CM Making sense of non-Hermitian Hamiltonians. Rep. Prog. Phys. 70947–1018 (2007).
Özdemir, Ş. K., Rotter, S., Nori, F. & Yang, L. Parity–time symmetry and exceptional points in photonics. Nat. Mater. 18783–798 (2019).
Miri, M.-A. & Alù, A. Exceptional points in optics and photonics. Science 363eaar7709 (2019).
Wang, K. et al. Generating arbitrary topological windings of a non-Hermitian band. Science 3711240–1245 (2021).
Wang, K., Dutt, A., Wojcik, CC & Fan, S. Topological complex-energy braiding of non-Hermitian bands. Nature 59859–64 (2021).
Gao, T. et al. Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiard. Nature 526554–558 (2015).
Zhong, Q., Khajavikhan, M., Christodoulides, DN & El-Ganainy, R. Winding around non-Hermitian singularities. Nat. Common. 94808 (2018).
Tang, W. et al. Exceptional nexus with a hybrid topological invariant. Science 3701077–1080 (2020).
Tang, W., Ding, K. & Ma, G. Direct measurement of topological properties of an exceptional parabola. Phys. Rev. Lett. 127034301 (2021).
Tang, W., Ding, K. & Ma, G. Experimental realization of non-Abelian permutations in a three-state non-Hermitian system. Preprint at https://doi.org/10.48550/arXiv.2112.00982 (2022).
Ghatak, A., Brandenbourger, M., van Wezel, J. & Coulais, C. Observation of non-Hermitian topology and its bulk–edge correspondence in an active mechanical metamaterial. proc. Natl Acad. Science. USA 11729561–29568 (2020).
Zhang, L. et al. Acoustic non-Hermitian skin effect from twisted winding topology. Nat. Common. 126297 (2021).
Weidemann, S. et al. Topological funneling of light. Science 368311–314 (2020).
Xiao, L. et al. Non-Hermitian bulk–boundary correspondence in quantum dynamics. Nat. Phys. 16761–766 (2020).
Song, F., Yao, S. & Wang, Z. Non-Hermitian topological invariants in real space. Phys. Rev. Lett. 123246801 (2019).
Longhi, S. Probing non-Hermitian skin effect and non-Bloch phase transitions. Phys. Rev. Res. 1023013 (2019).
Gao, P., Willatzen, M. & Christensen, J. Anomalous topological edge states in non-Hermitian piezophononic media. Phys. Rev. Lett. 125206402 (2020).
Zhu, W., Teo, WX, Li, L. & Gong, J. Delocalization of topological edge states. Phys. Rev. B 103195414 (2021).
Brandenbourger, M., Locsin, X., Lerner, E. & Coulais, C. Non-reciprocal robotic metamaterials. Nat. Common. 104608 (2019).
Hsu, CW, Zhen, B., Stone, AD, Joannopoulos, JD & Soljačić, M. Bound states in the continuum. Nat. Rev. Mater. 116048 (2016).
Okuma, N., Kawabata, K., Shiozaki, K. & Sato, M. Topological origin of non-Hermitian skin effects. Phys. Rev. Lett. 124086801 (2020).
Zhang, K., Yang, Z. & Fang, C. Correspondence between winding numbers and skin modes in non-Hermitian systems. Phys. Rev. Lett. 125126402 (2020).
Xiao, L. et al. Observation of non-Bloch parity-time symmetry and exceptional points. Phys. Rev. Lett. 126230402 (2021).
Sounas, DL & Alù, A. Non-reciprocal photonics based on time modulation. Nat. Photonics 11774–783 (2017).
Nassar, H. et al. Nonreciprocity in acoustic and elastic materials. Nat. Rev. Mater. 5667–685 (2020).
Painter, O. et al. Two-dimensional photonic band-gap defect laser mode. Science 2841819–1821 (1999).
Hirose, K. et al. Watt-class high-power, high-beam-quality photonic-crystal lasers. Nat. Photonics 8406–411 (2014).
Zhang, W. et al. Low-threshold topological nanolasers based on the second-order corner state. Light: Sci. Appl. 9109 (2020).
Teo, WX, Zhu, W. & Gong, J. Tunable two-dimensional laser arrays with zero-phase locking. Phys. Rev. B 105L201402 (2022).
Zhao, H. et al. Topological hybrid silicon microlasers. Nat. Common. 9981 (2018).
Kim, H.-R. et al. Multipolar lasing modes from topological corner states. Nat. Common. 115758 (2020).
Shao, Z.-K. et al. A high-performance topological bulk laser based on band-inversion-induced reflection. Nat. Nanotechnology. 1567–72 (2020).
Fan, S., Suh, W. & Joannopoulos, JD Temporal coupled-mode theory for the Fano resonance in optical resonators. J. Opt. Soc. Am.A 20569 (2003).
Chong, YD, Ge, L., Cao, H. & Stone, AD Coherent perfect absorbers: time-reversed lasers. Phys. Rev. Lett. 105053901 (2010).