Topological states of non-Hermitian systems

Abstract

Recently, the search for topological states of matter has turned to non-Hermitian systems, which exhibit a rich variety of unique properties without Hermitian counterparts. Lattices modeled through non-Hermitian Hamiltonians appear in the context of photonic systems, where one needs to account for gain and loss, circuits of resonators, and also when modeling the lifetime due to interactions in condensed matter systems. Here we provide a brief overview of this rapidly growing subject, the search for topological states and a bulk-boundary correspondence in non-Hermitian systems.

Perspective on topological states of non-Hermitian lattices

“…Non-Hermiticity however, does not necessarily lead to a complex spectrum [23,50]. If a Hamiltonian has  symmetry 3 and that symmetry is preserved by the eigenstates then the corresponding eigenvalues are real [23].…”

“…Together with Floquet systems, non-Hermitian lattices represent our first strong steps on the land of nonequilibrium, dynamical, topological phases. The departure from the Hermitian paradigm brings many surprises, like the fact that because of the extreme sensitivity to boundary conditions, a pristine non-Hermitian lattice may become devoid of extended states [47,48], an effect termed the non-Hermitian skin effect [49,50].…”

Anomalous features of non-Hermitian topological states

“…Topological band theory and its non-Hermitian extension have attracted great attention in the past decades [1][2][3][4][5][6]. The periodic table of Hermitian topological insulators is well-known, but its non-Hermitian counterpart has not yet been fully constructed.…”

Topological states in a non-Hermitian two-dimensional Su-Schrieffer-Heeger model

“…The past few years have witnessed a growing amount of interest in the theory of non-Hermitian extension of topological insulators [1,2]. A Combination of long-lived quantum states immune to decoherence and the unique features of non-Hermitian systems make non-Hermitian topological systems a promising platform for future applications in quantum technology.…”