Electron cooling by diffusive normal metal–superconductor tunnel junctions

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 doublebarrier SINIS microcooler.

Andreev current for low temperature thermometry

“…19,20 _ Q qp ðV; T e Þ represents the heating (or cooling) due to quasi-particle transport through one of the junctions. One can neglect this term near zero bias, but it dominates the left-hand side of Eq.…”

Electron cooling in diffusive normal metal–superconductor tunnel junctions with a spin-valve ferromagnetic interlayer

“…In what follows we assume that the temperatures of the S and N reservoirs to be equal, T S = T N = T , and neglect nonequilibrium effects in the ferromagnetic interlayer. 17 The bias voltage between the S and N reservoirs is an easily adjustable experimental parameter, so all our curves except those presented in Fig. 5 are calculated for optimal value of the voltage bias V opt , at which the cooling power reaches its maximum for given values of the other parameters.…”

“…(17,18,19) it is clear that for equal temperature of the electrodes (T N = T S ) and no bias voltage the cooling power vanishes. For a finite voltage V , on one hand the heat is taken from the N reservoir and is released in the superconductor.…”

“…At low enough temperatures this heating exceeds the single-particle cooling. [15][16][17] The interplay between the single-particle tunneling and Andreev reflection sets a limiting temperature for the refrigeration T min . 17 One way to decrease T min is to decrease the NIS junction transparency.…”

“…[15][16][17] The interplay between the single-particle tunneling and Andreev reflection sets a limiting temperature for the refrigeration T min . 17 One way to decrease T min is to decrease the NIS junction transparency. However, large values of the contact resistance hinder carrier transfer and lead to a severe limitation in the achievable cooling powers.…”