Emergence of the non-Hermitian topology in generalized eigenvalue problems with Hermitian matrices

Topological band theory has been studied as one of the central issues of condensed matter physics in these fifteen years. It has been initiated as the eigenvalue problems of a Hermitian matrix [1,2], which has revealed many non-trivial phenomena such as bulk-boundary correspondence [3]. Notably, recent studies have extended the framework of the topological band theory to the non-Hermitian eigenvalue problems [4,5,6]. This extension reveals the existence of the topological phenomena unique to the non-Hermitian systems.



In this talk, we attempt a further extension of the topological band theory: extension of topological band theory to the generalized eigenvalue problem [7]. In particular, we elucidate the emergence of the symmetry-protected non-Hermitian topological band structure without non-Hermitian matrices. After that discussion, we analyze a toy model and apply our theory to an optical system.



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[3] Y. Hatsugai, Phys. Rev. Lett. 71, 3697 (1993).

[4] K. Esaki, M. Sato, K. Hasebe, and M. Kohmoto, Phys. Rev. B 84, 205128 (2011).

[5] H. Shen, B. Zhen, and L. Fu, Phys. Rev. Lett. 120, 146402 (2018).

[6] Z. Gong, Y. Ashida, K. Kawabata, K. Takasan, S. Higashikawa, and M. Ueda, Phys. Rev. X 8, 031079 (2018).

[7] T. Isobe, T. Yoshida, and Y. Hatsugai, Phys. Rev. B 104, L121105 (2021).