Topological phases and nonreciprocal edge states in non-Hermitian Floquet Insulators

Abstract

Topological phases in quantum and classical systems have been of significant recent interest due to their fascinating physical properties. While a range of different mechanisms to induce topological order have been introduced, a quest for the most viable solution for practical systems is still open. Floquet topological insulator represent one of possible venues to engineer topological phases, yet they have been so far largely restricted to temporal modulation of Hermitian potentials. On the other hand, in many physical systems, including acoustic and optical systems, modulating loss or gain can be more straightforwardly achieved. Two of such examples are graphene, which enables strong modulation of its conductivity due to saturable absorption, and quantum wells where population inversion can be achieved in an ultrafast manner. On the other hand, non-Hermitian Floquet potentials have not been shown to yield novel topological phases to date. It is therefore of great interest to explore time-modulated non-Hermitian potentials in periodic lattices, and the emergence of topological phases associated with them. Here we demonstrate that non-Hermitian Hamiltonians can indeed result in topological phases supporting nonreciprocal edge states propagating without dissipation, as well as new regimes of dissipative and amplifying topological edge transport.