The fate of high winding number topological phases in the disordered extended Su-Schrieffer-Heeger model

TL;DR

This paper investigates the robustness of high winding number topological phases in a disordered extended SSH model using Lindblad equations, revealing how disorder affects edge states and phase stability.

Contribution

It introduces a non-equilibrium steady state approach to analyze the stability of complex topological phases with multiple edge states under various disorder conditions.

Findings

High winding number phases can host multiple localized edge states.

Disorder can either preserve or destroy topological edge modes depending on symmetry.

The robustness of edge states varies with disorder type and strength.

Abstract

We use the Lindblad equation approach to investigate topological phases hosting more than one localized state at each side of a disordered SSH chain with properly tuned long range hoppings. Inducing a non equilibrium steady state across the chain, we probe the robustness of each phase and the fate of the edge modes looking at the distribution of electrons along the chain and the corresponding standard deviation in the presence of different kinds of disorder either preserving, or not, the symmetries of the Hamiltonian.