Interplay between long range hopping and disorder in topological systems

TL;DR

This paper investigates how long-range hopping and disorder influence the topological and electronic properties of an extended SSH model, revealing effects on symmetry, localization, and topological invariants with implications for transport.

Contribution

It introduces an extended SSH model with long-range hopping and disorder, analyzing their combined effects on topology and localization, and links Lyapunov exponents to topological features.

Findings

Long-range hopping alters symmetry class and topological invariants.

Disorder induces Anderson localization in the system.

Lyapunov exponent relates to topological properties and edge modes.

Abstract

We extend the standard SSH model to include long range hopping and disorder, and study how the electronic and topological properties are affected. We show that long range hopping can change the symmetry class and the topological invariant, while diagonal and off-diagonal disorder lead to Anderson localization. Interestingly we find that the Lyapunov exponent $\gamma(E)$ can be linked in two ways to the topological properties in the presence of disorder: Either due to the different response of mid-gap states to increasing disorder, or due to an extra contribution to $\gamma$ due to the presence of edge modes. Finally we discuss its implications in realistic transport measurements.