Phase coherence, inelastic scattering, and interaction corrections in pumping through quantum dots

TL;DR

This paper develops a formalism to analyze adiabatic quantum pumping in interacting, phase-coherent quantum dots, accounting for inelastic scattering and interaction effects that go beyond Brouwer's formula, with applications to bosonic baths and charge quantization.

Contribution

It introduces a controlled adiabatic expansion formalism to include interaction effects in quantum pumping, extending beyond Brouwer's phase-coherent description.

Findings

Interaction corrections describe inelastic scattering effects.

The formalism applies to bosonic bath interactions.

Quantization robustness is discussed in turnstile cycles.

Abstract

Adiabatic quantum pumping in noninteracting, phase coherent quantum dots is elegantly described by Brouwer's formula. Interactions within the dot, while suppressing phase coherence, make Brouwer's formalism inapplicable. In this paper, we discuss the nature of the physical processes forcing a description of pumping beyond Brouwer's formula, and develop, using a controlled adiabatic expansion, a useful formalism to study the effect of interactions within a generic perturbative scheme. The pumped current consists of a first contribution, analogous to Brouwer's formula and accounting for the remanent coherence, and of interaction corrections describing inelastic scattering. We apply the formalism to study the effect of interaction with a bosonic bath on a resonant level pump and discuss the robustness of the quantization of the pumped charge in turnstile cycles.