Competition between band topology and non-Hermiticity

The introduction of non-Hermiticity to topological systems profoundly modifies their topological properties, leading to unprecedented phenomena beyond the descriptions of Bloch band theory, e.g., the breakdown of the conventional bulk-boundary correspondence. However, the comprehensive interplay between band topology and non-Hermiticity remains elusive. Here, based on a non-Hermitian Su-Schrieffer-Heeger model, we demonstrate that in the non-Hermitian topological systems, band topology and non-Hermiticity interplay by competing with each other, exhibiting a transition from symmetry dominance to non-Hermitian dominance. The former is featured with two edge states separately distributed at the two ends of the Su-Schrieffer-Heeger chain, similar to their Hermitian counterparts. In the latter, however, driven by non-Hermiticity, the two edge states become localized toward the same chain end, exhibiting the non-Hermitian skin effect. We find that such a transition is a universal behavior in the non-Hermitian systems, which is responsible for the breakdown of the conventional bulk-boundary correspondence and is the key factor to understanding the non-Hermitian topological properties. Furthermore, it is shown that this transition can be modified by the mode coupling between the edge states. As a comparison, we propose a non-Hermitian square-root Su-Schrieffer-Heeger model, where the edge states do not couple with each other and the mode coupling effect can be deactivated. Our work explicitly reveals the interplay between band topology and non-Hermiticity, which lays the foundation for the studies of non-Hermitian topological physics.