Pauli blocking factors in quantum pumps

TL;DR

This paper demonstrates that in quantum pumps with coherent scattering, the Pauli blocking factor is unnecessary for calculating pumped currents, even when time-dependent potentials break micro-reversibility.

Contribution

It shows that the Pauli blocking factor can be omitted in coherent quantum pumping calculations using Floquet formalism.

Findings

Pumped currents can be derived without Pauli blocking factor.

Coherent scattering states form a complete non-orthogonal set.

Time-dependent potentials break micro-reversibility but do not require Pauli blocking.

Abstract

We investigate the Pauli blocking factor in quantum pumps using Floquet formalism. Even though the time dependent potentials in quantum pumping can not only cause inelastic scatterings but also break the micro-reversibility, i.e. $T^+(E',E) \neq T^-(E,E')$, the Pauli blocking factor is unnecessary when the scattering process through the scatterer is coherent. The well defined scattering states extending from one reservoir to the others form a complete non-orthogonal set. Regardless of the non-orthogonality one can obtain the pumped currents using the field operator formalism. The current expression finally obtained do not contain Pauli blocking factor.