Non-Hermitian generalizations of extended Su-Schrieffer-Heeger models

TL;DR

This paper explores non-Hermitian extensions of extended SSH models, revealing new topological features, localized states, and the non-Hermitian skin effect, with implications for experimental realization.

Contribution

It introduces non-Hermitian generalizations of SSH3 and SSH4 models, analyzing their topological properties and boundary phenomena, and clarifies the bulk-boundary correspondence in these systems.

Findings

Non-Hermitian SSH3 model exhibits a point-gap topology and skin effect.

SSH4 model's non-Hermitian version also shows skin effect and restored bulk-boundary correspondence.

Total Zak phase quantization indicates coexistence of localized states.

Abstract

Non-Hermitian generalizations of the Su-Schrieffer-Heeger (SSH) models with higher periods of the hopping coefficients, called the SSH3 and SSH4 models, are analyzed. The conventional construction of the winding number fails for the Hermitian SSH3 model, but the non-Hermitian generalization leads to a topological system due to a point gap on the complex plane. The non-Hermitian SSH3 model thus has a winding number and exhibits the non-Hermitian skin effect. Moreover, the SSH3 model has two types of localized states and a zero-energy state associated with special symmetries. The total Zak phase of the SSH3 model exhibits quantization, and its finite value indicates coexistence of the two types of localized states. Meanwhile, the SSH4 model resembles the SSH model, and its non-Hermitian generalization also exhibits the non-Hermitian skin effect. A careful analysis of the non-Hermitian SSH4 model with different boundary conditions shows the bulk-boundary correspondence is restored with the help of the generalized Brillouin zone or the real-space winding number. The physics of the non-Hermitian SSH3 and SSH4 models may be tested in cold-atom or other simulators.