Quantised adiabatic charge transport in the presence of substrate disorder and many-body interaction

The charge transport induced in an electronic system by a substrate potential varying adiabatically and periodically in time is investigated theoretically, extending the analysis of Thouless (1983) to the case of substrate disorder and many-body interaction. The single-particle interaction is examined, and the results are expanded to the many-particle case; the quantization of the adiabatic transport is found to persist in both cases. The implications of this analysis for the integral and fractional quantized Hall effect are explored.