Semiclassical theory of a quantum pump

TL;DR

This paper develops a semiclassical theory for quantum pumps, analyzing how the Ehrenfest time influences the pumped current in ballistic quantum dots, revealing a non-suppressed current component when Ehrenfest time exceeds dwell time.

Contribution

It introduces a semiclassical framework to understand quantum pumping in ballistic quantum dots considering Ehrenfest time effects, a novel aspect in the field.

Findings

Pumped current depends on the relation between Ehrenfest time and dwell time.

A component of the pumped current persists even when Ehrenfest time is large.

The theory explains quantum interference effects in ballistic quantum dots.

Abstract

In a quantum charge pump, the periodic variation of two parameters that affect the phase of the electronic wavefunction causes the flow of a direct current. The operating mechanism of a quantum pump is based on quantum interference, the phases of interfering amplitudes being modulated by the external parameters. In a ballistic quantum dot, there is a minimum time before which quantum interference can not occur: the Ehrenfest time. Here we calculate the current pumped through a ballistic quantum dot when the Ehrenfest time is comparable to the mean dwell time. Remarkably, we find that the pumped current has a component that is not suppressed if the Ehrenfest time is much larger than the mean dwell time.