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

We study the stability of the topological phase in one-dimensional Su-Schrieffer-Heeger chain subject to the quasiperiodic hopping disorder. Two different hopping disorder configurations are investigated, one is the Aubry-André quasiperiodic disorder without mobility edges and the other is the slowly varying quasiperiodic disorder with mobility edges. Interestingly, we find topological phase transitions occur at the critical quasiperiodic disorder strengths which have an exact linear relation with the dimerization strengths 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.