Bender, C. M. & Boettcher, S. Real spectra in non-Hermitian Hamiltonians having PT symmetry. Phys. Rev. Lett. 80, 5243–5246 (1998).
Heiss, W. D. The physics of exceptional points. J. Phys. A 45, 444016 (2012).
Chen, H.-Z. et al. Revealing the missing dimension at an exceptional point. Nat. Phys. 16, 571–578 (2020).
Liu, T. et al. Chirality-switchable acoustic vortex emission via non-Hermitian selective excitation at an exceptional point. Sci. Bull. 67, 1131–1136 (2022).
Ashida, Y., Gong, Z. & Ueda, M. Non-Hermitian physics. Adv. Phys. 69, 249–435 (2020).
Bergholtz, E. J., Budich, J. C. & Kunst, F. K. Exceptional topology of non-Hermitian systems. Rev. Mod. Phys. 93, 015005 (2021).
Ding, K., Fang, C. & Ma, G. Non-Hermitian topology and exceptional-point geometries. Nat. Rev. Phys. 4, 745–760 (2022).
Bender, C. M. & Hook, D. W. PT-symmetric quantum mechanics. Rev. Mod. Phys. 96, 045002 (2024).
Feng, L., El-Ganainy, R. & Ge, L. Non-Hermitian photonics based on parity–time symmetry. Nat. Photonics 11, 752–762 (2017).
Özdemir, Ş. K., Rotter, S., Nori, F. & Yang, L. Parity–time symmetry and exceptional points in photonics. Nat. Mater. 18, 783–798 (2019).
Miri, M.-A. & Alù, A. Exceptional points in optics and photonics. Science 363, eaar7709 (2019).
Huang, L. et al. Acoustic resonances in non-Hermitian open systems. Nat. Rev. Phys. 6, 11–27 (2024).
Zhong, Q., Kou, J., Özdemir, Ş. K. & El-Ganainy, R. Hierarchical construction of higher-order exceptional points. Phys. Rev. Lett. 125, 203602 (2020).
Wiersig, J. Revisiting the hierarchical construction of higher-order exceptional points. Phys. Rev. A 106, 063526 (2022).
Wiersig, J. & Chen, W. Higher-order exceptional points in composite non-Hermitian systems. Phys. Rev. Res. 7, 033034 (2025).
Okuma, N. & Sato, M. Non-Hermitian topological phenomena: a review. Annu. Rev. Condens. Matter Phys. 14, 83–107 (2023).
Lin, R., Tai, T., Li, L. & Lee, C. H. Topological Non-Hermitian skin effect. Front. Phys. 18, 53605 (2023).
Yao, S. & Wang, Z. Edge states and topological invariants of non-Hermitian systems. Phys. Rev. Lett. 121, 086803 (2018).
Yang, Z., Zhang, K., Fang, C. & Hu, J. Non-Hermitian bulk-boundary correspondence and auxiliary generalized Brillouin zone theory. Phys. Rev. Lett. 125, 226402 (2020).
Zhang, K., Yang, Z. & Fang, C. Correspondence between winding numbers and skin modes in non-Hermitian systems. Phys. Rev. Lett. 125, 126402 (2020).
Seyranian, A. P. & Mailybaev, A. A. Multiparameter Stability Theory with Mechanical Applications (World Scientific, 2003).
Radjavi, H. & Rosenthal, P. Invariant Subspaces (Springer-Verlag, 1973).
Zhang, L. et al. Acoustic non-Hermitian skin effect from twisted winding topology. Nat. Commun. 12, 6297 (2021).
Yokomizo, K. & Murakami, S. Non-Bloch band theory of non-Hermitian systems. Phys. Rev. Lett. 123, 066404 (2019).
Wang, W., Wang, X. & Ma, G. Non-Hermitian morphing of topological modes. Nature 608, 50–55 (2022).
Wang, W., Wang, X. & Ma, G. Extended state in a localized continuum. Phys. Rev. Lett. 129, 264301 (2022).
Wang, W., Hu, M., Wang, X., Ma, G. & Ding, K. Experimental realization of geometry-dependent skin effect in a reciprocal two-dimensional lattice. Phys. Rev. Lett. 131, 207201 (2023).
Cui, X. et al. Experimental realization of stable exceptional chains protected by non-Hermitian latent symmetries unique to mechanical systems. Phys. Rev. Lett. 131, 237201 (2023).
Li, Z. et al. Observation of dynamic non-Hermitian skin effects. Nat. Commun. 15, 6544 (2024).
Wang, W., Wang, X. & Ma, G. Anderson transition at complex energies in one-dimensional parity-time-symmetric disordered systems. Phys. Rev. Lett. 134, 066301 (2025).
Wiersig, J. Response strengths of open systems at exceptional points. Phys. Rev. Res. 4, 023121 (2022).
Wiersig, J. Moving along an exceptional surface towards a higher-order exceptional point. Phys. Rev. A 108, 033501 (2023).
Okuma, N., Kawabata, K., Shiozaki, K. & Sato, M. Topological origin of non-Hermitian skin effects. Phys. Rev. Lett. 124, 086801 (2020).
Kawabata, K., Shiozaki, K., Ueda, M. & Sato, M. Symmetry and topology in non-Hermitian physics. Phys. Rev. X 9, 041015 (2019).
Gao, H., Zhu, W., Xue, H., Ma, G. & Su, Z. Controlling acoustic non-Hermitian skin effect via synthetic magnetic fields. Appl. Phys. Rev. 11, 031410 (2024).
Teo, H. T., Mandal, S., Long, Y., Xue, H. & Zhang, B. Pseudomagnetic suppression of non-Hermitian skin effect. Sci. Bull. 69, 1667–1673 (2024).
Hatano, N. & Nelson, D. R. Localization transitions in non-Hermitian quantum mechanics. Phys. Rev. Lett. 77, 570–573 (1996).
Shi, Y. B., Zhang, K. L. & Song, Z. Exceptional spectrum and dynamic magnetization. J. Phys.: Condens. Matter 34, 485401 (2022).
Wang, S. et al. Arbitrary order exceptional point induced by photonic spin–orbit interaction in coupled resonators. Nat. Commun. 10, 832 (2019).
Chen, Z. et al. Sound non-reciprocity based on synthetic magnetism. Sci. Bull. 68, 2164–2169 (2023).
Su, L. et al. Observation of size-dependent boundary effects in non-Hermitian electric circuits. Chin. Phys. B 32, 038401 (2023).
Guo, C.-X. et al. Scale-tailored localization and its observation in non-Hermitian electrical circuits. Nat. Commun. 15, 9120 (2024).
Chen, W., Kaya Özdemir, Ş., Zhao, G., Wiersig, J. & Yang, L. Exceptional points enhance sensing in an optical microcavity. Nature 548, 192–196 (2017).
Doppler, J. et al. Dynamically encircling an exceptional point for asymmetric mode switching. Nature 537, 76–79 (2016).
Feng, L., Wong, Z. J., Ma, R.-M., Wang, Y. & Zhang, X. Single-mode laser by parity-time symmetry breaking. Science 346, 972–975 (2014).
Kawabata, K., Bessho, T. & Sato, M. Classification of exceptional points and non-Hermitian topological semimetals. Phys. Rev. Lett. 123, 066405 (2019).
Wojcik, C. C., Sun, X.-Q., Bzdušek, T. & Fan, S. Homotopy characterization of non-Hermitian Hamiltonians. Phys. Rev. B 101, 205417 (2020).
Li, Z. & Mong, R. S. K. Homotopical characterization of non-Hermitian band structures. Phys. Rev. B 103, 155129 (2021).
Tang, W. et al. Exceptional nexus with a hybrid topological invariant. Science 370, 1077–1080 (2020).
Tang, W., Ding, K. & Ma, G. Experimental realization of non-abelian permutations in a three-state non-Hermitian system. Natl Sci. Rev. 9, nwac010 (2022).
Tang, W., Ding, K. & Ma, G. Realization and topological properties of third-order exceptional lines embedded in exceptional surfaces. Nat. Commun. 14, 6660 (2023).
Yang, K. et al. Homotopy, symmetry, and non-Hermitian band topology. Rep. Prog. Phys. 87, 078002 (2024).
Lee, C. H. Exceptional bound states and negative entanglement entropy. Phys. Rev. Lett. 128, 010402 (2022).
Li, Z. et al. Exceptional deficiency of non-Hermitian systems. Zenodo https://doi.org/10.5281/zenodo.19494159 (2026).