Floquet topological properties in the Non-Hermitian long-range system with complex hopping amplitudes

TL;DR

This paper explores Floquet topological phases in a non-Hermitian, periodically driven system with complex long-range hopping, revealing how phase changes induce topological transitions and how imaginary hopping terms enrich the phase diagram.

Contribution

It demonstrates the connection between winding numbers and edge states in non-Hermitian Floquet systems and uncovers the effects of phase and imaginary hopping on topological phases.

Findings

Winding number correlates with edge states despite non-Hermiticity.

Phase of hopping amplitude induces topological phase transitions.

Imaginary hopping term creates a rich phase diagram.

Abstract

Non-equilibrium phases of matter have attracted much attention in recent years, among which the Floquet phase is a hot point. In this work, based on the Periodic driving Non-Hermitian model, we reveal that the winding number calculated in the framework of the Bloch band theory has a direct connection with the number of edge states even the Non-Hermiticity is present. Further, we find that the change of the phase of the hopping amplitude can induce the topological phase transitions. Precisely speaking, the increase of the value of the phase can bring the system into the larger topological phase. Moreover, it can be unveiled that the introduction of the purely imaginary hopping term brings an extremely rich phase diagram. In addition, we can select the even topological invariant exactly from the unlimited winding numbers if we only consider the next-nearest neighbor hopping term. Here, the results obtained may be useful for understanding the Periodic driving Non-Hermitian theory.