Topological phase transition of generalized Brillouin zone in Hermitian and non-Hermitian systems
일 시 : 2024년 07월 01일 월요일 14:00
연 사 : Sonu Verma 박사 (Institute for Basic Science)
장 소 : 자연과학관 B115호
초 록
A generic feature of symmetry-protected topological (SPT) phases of matter is the bulk-boundary correspondence (BBC), which connects the concept of bulk topology to the emergence of robust boundary states. In recent years, non-Hermitian systems have shown unconventional properties and phenomena such as exceptional points, non-Hermitian skin effect, and many more in different research fields without Hermitian analogs. Therefore, the topological Bloch band theory with the notion of the Brillouin zone (BZ) has been extended to the non-Bloch band theory with the idea of the generalized Brillouin zone (GBZ) defined by generalized momenta, which can take complex values. The non-Bloch band theory has successfully proven that non-Hermitian systems show two types of modified BBC: (i) complex eigenvalue topology of the bulk leads to non-Hermitian skin effect, where all bulk states localize at one boundary of the system, and (ii) the eigenstate topology in the GBZ leads to the conventional topological boundary modes. In this seminar, I will discuss our recent finding of a new type of BBC in non-Hermitian systems [1] that originates from the intrinsic topology of the GBZ. Topologically non-trivial GBZ appears due to generalized boundary conditions that locally break the system's translation symmetry. In our case, the topological phase transition is characterized by the generalized momentum touching of GBZ, which accompanies the emergence of exceptional points. I will also discuss extending our work to Hermitian systems [2]. Firstly, we found that the intrinsic topology of GBZ successfully characterizes the SPT phases. In this case, the topological phase transition of GBZ is characterized by the generalized momenta touching of GBZ, which accompanies the emergence of band touching points. Moreover, the non-Bloch band theory provides a natural topological invariant characterizing the sub-symmetry-protected topological phases that conventional Bloch topological invariants generally fail to describe.
References: [1] Sonu Verma and Moon Jip Park, Communications Physics 7, 21 (2024). [2] Sonu Verma and Moon Jip Park, arXiv:2405.06240.