Floquet-Anderson localization in the Thouless pump and how to avoid it

TL;DR

This paper studies how disorder affects the quantized charge transport in the Floquet-driven Rice-Mele model, revealing conditions under which Anderson localization can be avoided in the thermodynamic limit.

Contribution

It introduces a specific thermodynamic limit where Anderson localization can be circumvented, ensuring robust charge pumping despite disorder.

Findings

Increasing system size leads to pump breakdown at fixed parameters.

A modified thermodynamic limit prevents localization, maintaining quantized charge transport.

The critical exponent for localization depends on disorder strength.

Abstract

We investigate numerically how onsite disorder affects conduction in the periodically driven Rice-Mele model, a prototypical realization of the Thouless pump. Although the pump is robust against disorder in the fully adiabatic limit, much less is known about the case of finite period time $T$, which is relevant also in light of recent experimental realizations. We find that at any fixed period time and nonzero disorder, increasing the system size $L\to\infty$ always leads to a breakdown of the pump, indicating Anderson localization of the Floquet states. Our numerics indicate, however, that in a properly defined thermodynamic limit, where $L/T^\theta$ is kept constant, Anderson localization can be avoided, and the charge pumped per cycle has a well-defined value -- as long as the disorder is not too strong. The critical exponent $\theta$ is not universal, rather, its value depends on the disorder strength. Our findings are relevant for practical, experimental realizations of the Thouless pump, for studies investigating the nature of its current-carrying Floquet eigenstates, as well as the mechanism of the full breakdown of the pump, expected if the disorder exceeds a critical value.