Exact Mobility Edges and Topological Anderson Insulating Phase in a Slowly Varying Quasiperiodic Model

Abstract

The relationship of topology and disorder in a 1D Su-Schrieffer-Heeger chain subjected to a slowly varying quasi-periodic modulation is uncovered. By numerically calculating the disorder-averaged winding number and analytically studying the localization length of the zero modes, the topological phase diagram is obtained, which implies that the topological Anderson insulator (TAI) can be induced by a slowly varying quasi-periodic modulation. Moreover, unlike the localization properties in the TAI phase caused by random disorder, mobility edges can enter into the TAI region identified by the fractal dimension, the inverse participation ratio, and the spatial distributions of the wave functions, the boundaries of which coincide with the analytical results presented here.

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“…The well-known Aubry-André (AA) model, due to its self-duality property, exhibits no mobility edge, with the system being either in an extended or localized state depending on whether the quasiperiodic strength is below or above the critical value, respectively [16]. Mobility edges can be observed in various generalized versions of the AA model by introducing short-range or longrange hopping interactions [17][18][19][20][21][22] or by modifying the quasiperiodic potentials [23][24][25][26][27][28][29][30][31][32][33][34][35].…”