Electron cooling by diffusive normal metal - superconductor tunnel junctions

TL;DR

This paper studies heat and charge transport in diffusive NN'IS tunnel junctions, revealing how Andreev reflection-induced Joule heating limits electron refrigeration at low temperatures.

Contribution

It provides a detailed analysis of heat transfer mechanisms in NN'IS junctions, highlighting the impact of Andreev reflection on cooling efficiency and the existence of a temperature limit.

Findings

Andreev reflection causes Joule heating that dominates at low temperatures.

A limiting temperature exists for effective electron refrigeration.

Results are applicable to various contact geometries and SINIS microcoolers.

Abstract

We investigate heat and charge transport in NN'IS tunnel junctions in the diffusive limit. Here N and S are massive normal and superconducting electrodes (reservoirs), N' is a normal metal strip, and I is an insulator. The flow of electric current in such structures at subgap bias is accompanied by heat transfer from the normal metal into the superconductor, which enables refrigeration of electrons in the normal metal. We show that the two-particle current due to Andreev reflection generates Joule heating, which is deposited in the N electrode and dominates over the single-particle cooling at low enough temperatures. This results in the existence of a limiting temperature for refrigeration. We consider different geometries of the contact: one-dimensional and planar, which is commonly used in the experiments. We also discuss the applicability of our results to a double-barrier SINIS microcooler.