Topological properties of non-Hermitian Creutz Ladders

TL;DR

This paper investigates the topological phases and non-Hermitian skin effects in a non-Hermitian Creutz ladder model, revealing complex behaviors and conditions under which bulk-boundary correspondence is preserved or broken.

Contribution

It provides a detailed analysis of the topological properties and skin effects in a non-Hermitian Creutz ladder, highlighting new phenomena and conditions distinct from Hermitian systems.

Findings

Topological winding exists in a 2D plane within a 4D complex Hamiltonian space.

Unusual non-Hermitian skin effects include high spectral winding without long-range hoppings.

The bulk-boundary correspondence can be preserved or broken depending on band gap closure at exceptional points.

Abstract

In this work we study topological properties of the one-dimensional Creutz ladder model with different non-Hermitian asymmetric hoppings and on-site imaginary potentials, and obtain phase diagrams regarding the presence and absence of an energy gap and in-gap edge modes. The non-Hermitian skin effect (NHSE), which is known to break the bulk-boundary correspondence (BBC), emerges in the system only when the non-Hermiticity induces certain unbalanced non-reciprocity along the ladder. The topological properties of the model are found to be more sophisticated than that of its Hermitian counterpart, whether with or without the NHSE. In one scenario without the NHSE, the topological winding is found to exist in a two-dimensional plane embedded in a four-dimensional space of the complex Hamiltonian vector. The NHSE itself also possesses some unusual behaviors in this system, including a high spectral winding without the presence of long-range hoppings, and a competition between two types of the NHSE, with the same and opposite inverse localization lengths for the two bands, respectively. Furthermore, it is found that the NHSE in this model does not always break the conventional BBC, which is also associated with whether the band gap closes at exceptional points under the periodic boundary condition.