Non-adiabatic effect on Laughlin's argument of the quantum Hall effect

TL;DR

This paper numerically investigates non-adiabatic charge transport in quantum Hall systems, revealing how pumped charge transitions from quantized to zero as the system moves from adiabatic to sudden limits, influenced by the Landau gap.

Contribution

It introduces a formula linking adiabatic quantized pumping and no-pumping in the sudden limit, considering non-adiabatic effects and impurity influences.

Findings

Quantized charge pumping occurs in the adiabatic limit.

Charge pumping diminishes in the sudden limit.

Landau gap determines the transition between regimes.

Abstract

We have numerically studied a non-adiabatic charge transport in the quantum Hall system pumped by a magnetic flux, as one of the simplest theoretical realizations of non-adiabatic Thouless pumping. In the adiabatic limit, a pumped charge is quantized, known as Laughlin's argument in a cylindrical lattice. In a uniform electric field, we obtained a formula connecting quantized pumping in the adiabatic limit and no-pumping in the sudden limit. The intermediate region between the two limits is determined by the Landau gap. A randomness or impurity effect is also discussed.