Topological Phase Transitions of Generalized Brillouin Zone in non-Hermitian systems

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 analog. In these systems the notion of Brillouin zone (BZ) has been extended to generalized Brillouin zone (GBZ) defined by generalized momenta which can take complex values . A generic feature of topological phases of matter is the bulk-boundary correspondence (BBC) which connects the concept of bulk topology to the emergence of robust boundary states. Recent studies prove that non-Hermitian systems show two types of modified BBC: (i) complex energy topology of the bulk leads to non-Hermitian skin effect, where all bulk states localize at one boundary of the system, and (ii) wave function topology leads to the conventional topological boundary modes.

In this seminar, I will discuss our recent finding of a new type of BBC, which originates from the intrinsic topology of the GBZ. Topologically non-trivial GBZ appear due to general boundary conditions that break the translation symmetry of the system. In our case, the topological phase transition is characterized by the generalized momentum touching of GBZ, which accompanies the emergence of exceptional points.