Cutting off the non-Hermitian boundary from an anomalous Floquet topological insulator

Understand

In two-dimensional anomalous Floquet insulators, non-Hermitian boundary state engineering can be used to completely separate chiral boundary states from bulk bands in the quasienergy spectrum.

• The topological properties of such spectrally separated boundary states are no longer restricted by the strict bulk-boundary correspondence of Hermitian systems.
• We show that this additional topological freedom enables one to faithfully transfer the topological properties of a boundary attached to a Floquet insulator to a non-Hermitian Floquet chain obtained by physically cutting off the boundary from the bulk.
• We implement this scenario for a simple model of an anomalous Floquet insulator with Hermitian and non-Hermitian boundaries, and discuss the relevance of our construction for the experimental realization of non-Hermitian topological phases that connect dimensions one and two.