Novel mobility edges in the off-diagonal disordered tight-binding models

TL;DR

This paper investigates one-dimensional tight-binding models with off-diagonal disorder, revealing the conditions for mobility edges and how they are affected by combined diagonal and off-diagonal disorder, supported by analytical and numerical analysis.

Contribution

It provides the first exact expressions for mobility edges in off-diagonal disordered models and explores their behavior under combined disorder types.

Findings

Mobility edges appear only with off-diagonal disorder.

Locations of mobility edges shift significantly with combined disorder.

Numerical diagnostics confirm analytical predictions.

Abstract

We study the one-dimensional tight-binding models which include a slowly varying, incommensurate off-diagonal modulation on the hopping amplitude. Interestingly, we find that the mobility edges can appear only when this off-diagonal (hopping) disorder is included in the model, which is different from the known results induced by the diagonal disorder. We further study the situation where the off-diagonal and diagonal disorder terms (the incommensurate potential) are both included and find that the locations of mobility edges change significantly and the varying trend of the mobility edge becomes nonsmooth. We first identify the exact expressions of mobility edges of both models by using asymptotic heuristic argument, and then verify the conclusions by utilizing several numerical diagnostic techniques, including the inverse participation ratio, the density of states and the Lyapunov exponent. This result will perspectives for future investigations on the mobility edge in low dimensional correlated disordered system.