Defect-position-dependent -symmetry breaking in coupled Su–Schrieffer–Heeger chains

Abstract

We investigate the spontaneous parity-time (-) symmetry-breaking behavior under three different cases in three coupled Su–Schrieffer–Heeger chains whose Hermiticity is broken by the presence of two conjugated imaginary potentials (defect terms). We show that the defect terms located at different positions in the system have significant impacts on the energy spectra in topologically trivial and nontrivial regimes. Meanwhile, we find that the topologically nontrivial zero-energy edge modes exist in symmetric region and the system undergoes several -symmetry-breaking transitions when the defect terms are located at the middle positions. Interestingly, when the defect terms are located at each position, the symmetry of the system is always spontaneously broken no matter how the loss rate changes. Under the same parameter regimes, furthermore, the energy spectra of the system for the cases that the defect terms are located at the two end positions and at the middle positions are more robust than to the case that the defect terms are located at each position.