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

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