Fate of pseudomobility edges and multiple states in a non-Hermitian Wannier-Stark lattice
Yu‐Jun Zhao, Han-Ze Li, Xuyang Huang, Shan-Zhong Li, Jianxin Zhong
Abstract
The interaction between nonreciprocity and disorder-free localization has emerged as a fascinating open question. Here, we explore the effects of pseudomobility edges along with different types of eigenstates in a one-dimensional lattice subjected to a nonreciprocal finite-height Wannier-Stark ladder. Utilizing the transfer matrix method, we analytically investigate the pseudomobility edges under nonreciprocity, which accurately describes the boundary between ergodic and nonergodic states. The ergodic states, under nonreciprocity, form topological point gaps in the complex plane, with the corresponding eigenstates localized at the boundaries. The localization of mixed states induced by the skin effect and Wannier-Stark ladder is further amplified under nonreciprocity. Through similarity transformations, the fate of multiple eigenstates under nonreciprocal transitions can be captured. Finally, we use wave packet dynamics as a means to detect these emerging states. Our findings broaden the understanding of disorder-free localization in non-Hermitian systems.