Nonequilibrium electron cooling by NIS tunnel junctions

TL;DR

This paper develops a theoretical framework using quasiclassical equations to analyze quasiparticle electric and heat currents in NIS tunnel junctions, highlighting the impact of inelastic relaxation and backtunneling on cooling performance.

Contribution

It introduces a detailed theoretical model for diffusive NIS'S junctions, accounting for nonequilibrium effects and relaxation, advancing understanding of electron cooling mechanisms.

Findings

Suppression of electric current and cooling power without strong relaxation

Scaling of suppression with diffusive transparency parameter

Backtunneling of nonequilibrium quasiparticles causes suppression

Abstract

We discuss the theoretical framework to describe quasiparticle electric and heat currents in NIS tunnel junctions in the dirty limit. The approach is based on quasiclassical Keldysh-Usadel equations. We apply this theory to diffusive NIS'S tunnel junctions. Here N and S are respectively normal metal and superconductor reservoirs, I is an insulator layer and S' is a nonequilibrium superconducting lead. We calculate the quasiparticle electric and heat currents in such structures and consider the effect of inelastic relaxation in the S' lead. We find that in the absence of strong relaxation the electric current and the cooling power for voltages $eV < \Delta$ are suppressed. The value of this suppression scales with the diffusive transparency parameter. We ascribe this suppression to the effect of backtunneling of nonequilibrium quasiparticles into the normal metal.