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

Topological phases in quantum and classical systems have been of significant recent interest due to their fascinating physical properties. Floquet topological insulators represent one of the possible venues for engineering 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. On the other hand, non-Hermitian Floquet potentials have not been shown to yield any 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 regimes of dissipative and amplifying topological edge transport.