Real-potential-driven anti- -symmetry breaking in non-Hermitian Su–Schrieffer–Heeger model

Abstract

Non-Hermitian Hamiltonians with anti- $\mathcal{PT}$ symmetry show distinct discrepancies compared to $\mathcal{PT}$ -symmetric systems. Here we investigate the non-Hermitian Su–Schrieffer–Heeger (SSH) model and reveal the interplay between anti- $\mathcal{PT}$ symmetry and different topological phases, in which the anti- $\mathcal{PT}$ symmetry is triggered by introducing real chemical potential and imaginary nearest-neighbor hopping. Three types of anti- $\mathcal{PT}$ -symmetric SSH models with different on-site configurations are investigated, and the effect of each on-site configuration on the energy spectrum of system is analyzed and discussed. We find that the type of on-site configuration affects the energy spectrum of the same topological region significantly and each on-site configuration has distinguishable impacts on the energy spectra of different topological regions. Moreover, the spontaneous anti- $\mathcal{PT}$ -symmetry-breaking transitions undergone in both of the topologically trivial and nontrivial regions are also clarified. Furthermore, we address the corresponding eigenstates of some specific eigenvalues and some interesting localized phenomena are observed. Our results enrich the study of non-Hermitian topological phases and broaden the understanding of anti- $\mathcal{PT}$ -symmetric systems.

Keywords

• anti-PT-symmetry breaking
• topological phase
• Su–Schrieffer–Heeger model