Energy spectra of coupled Su-Schrieffer-Heeger chains with -symmetric imaginary boundary potentials

Abstract

We theoretically investigate the eigenenergies of coupled Su-Schrieffer-Heeger (SSH) chains with -symmetric imaginary potentials. It is found that the direct coupling between two SSH chains leads to the splitting of the topological edge states accompanied by the destruction of their original natures. If the two SSH chains are indirectly coupled via an impurity, additional nontopological isolated states are allowed to come up. Next when the -symmetric potentials are incorporated, the topological zero-energy states undergo the simple -symmetry breaking. However, the nontopological isolated states exhibit complicated variations. For the directly-coupled case, the phase transition of these states can be seen. Alternatively, in the indirectly-coupled SSH system, the partial -symmetry breaking occurs in the presence of broken particle-hole symmetry. We believe that these findings can be helpful for understanding topological properties of coupled non-Hermitian SSH systems.