Topological phase transition in the quasiperiodic disordered Su-Schriffer-Heeger chain

TL;DR

This paper investigates how quasiperiodic disorder affects the topological phases of a one-dimensional Su-Schrieffer-Heeger chain, revealing phase transitions and mobility edges influenced by disorder strength and dimerization.

Contribution

It introduces a detailed analysis of topological phase transitions under two types of quasiperiodic disorder, highlighting a linear relation between critical disorder strength and dimerization.

Findings

Topological phase transitions occur at a critical disorder strength linearly related to dimerization.

Mobility edges appear in the spectrum when dimerization is not equal to 1.

The study elucidates the interplay between topology and quasiperiodic disorder.

Abstract

We study the stability of the topological phase in one-dimensional Su-Schrieffer-Heeger chain subject to the quasiperiodic hopping disorder. We investigate two different hopping disorder configurations, one is the Aubry-Andr\'{e} quasiperiodic disorder without mobility edges and the other is the slowly varying quasiperiodic disorder with mobility edges. With the increment of the quasiperiodic disorder strength, the topological phase of the system transitions to a topologically trivial phase. Interestingly, we find the occurrence of the topological phase transition at the critical disorder strength which has an exact linear relation with the dimerization strength for both disorder configurations. We further investigate the localized property of the Su-Schrieffer-Heeger chain with the slowly varying quasiperiodic disorder, and identify that there exist mobility edges in the spectrum when the dimerization strength is unequal to 1. These interesting features of models will shed light on the study of interplay between topological and disordered systems.