Dynamic Moir\'{e}-like pattern in non-Hermitian Wannier-Stark ladder system

TL;DR

This paper investigates the dynamic behavior of a non-Hermitian Wannier-Stark ladder system, revealing how external fields induce distinct real and complex energy ladder regimes separated by exceptional points, with Moiré-like patterns emerging in non-linear fields.

Contribution

It introduces a non-Hermitian Floquet approach to analyze the Wannier-Stark ladder system, uncovering dynamic Moiré-like patterns and the interplay between $ ext{PT}$ symmetry and external fields.

Findings

Energy levels are sensitive to external fields.

Two distinct dynamic regimes separated by an exceptional point.

Moiré-like patterns emerge in non-linear field cases.

Abstract

We study the dynamical behavior of the non-Hermitian Wannier-Stark ladder system, which is a non-Hermitian Su-Schrieffer-Heeger chain with a position-dependent real potential. In the presence of a linear external field, we employ the non-Hermitian Floquet method and find that the energy levels are sensitive to the field. The system exhibits two distinct dynamic behaviors separated by an exceptional point: one in the $\mathcal{PT}$ symmetrical region associated with two real Wannier-Stark ladders, and another in the $\mathcal{PT}$\ symmetry-breaking region associated with complex conjugate ladders. As the boundary between the two regions, two ladders coalesce into a single ladder. In the case of a non-linear field, these two distinct regions appear alternately along the chain, exhibiting dynamic Moir\'{e}-like patterns.