Statistics of an adiabatic charge pump

TL;DR

This paper develops a nonequilibrium Green's function approach to analyze charge transport statistics in an adiabatic quantum pump, revealing Berry phase effects on current cumulants.

Contribution

It introduces a novel formalism for charge pumping statistics and highlights Berry phase contributions in a specific class of cyclic drivings.

Findings

Berry phase affects odd cumulants of pumped charge

Analytical expression for average pumped current derived

Quantum master equation does not capture Berry-phase effects

Abstract

We investigate the effect of time-dependent cyclic-adiabatic driving on the charge transport in quantum junction. We propose a nonequilibrium Greens function formalism to study statistics of the charge pumped (at zero bias) through the junction. The formulation is used to demonstrate charge pumping in a single electronic level coupled to two (electronic) reservoirs with time dependent couplings. Analytical expression for the average pumped current for a general cyclic driving is derived. It is found that for zero bias, for a certain class of driving, the Berry phase contributes only to the odd cumulants. To contrast, a quantum master equation formulation does not show Berry-phase effect at all.