Electron cooling by phonons in superconducting proximity structures

TL;DR

This paper develops a theoretical framework to analyze electron-phonon cooling in disordered superconducting proximity structures, revealing suppressed cooling at low temperatures and potential for quantum calorimetry applications.

Contribution

It provides a general expression for cooling power in out-of-equilibrium disordered systems, including novel geometries of superconductor-normal metal contacts.

Findings

Cooling power is significantly suppressed at low temperatures.

Proximity structures exhibit a minigap in the quasiparticle spectrum.

Structures are promising for quantum calorimetry due to tunability.

Abstract

We investigate the electron-phonon cooling power in disordered electronic systems with a special focus on mesoscopic superconducting proximity structures. Employing the quasiclassical Keldysh Green's function method, we obtain a general expression for the cooling power perturbative in the electron-phonon coupling, but valid for arbitrary electronic systems out of equilibrium. We apply our theory to several disordered electronic systems valid for an arbitrary relation between the thermal phonon wavelength and the electronic mean free path due to impurity scattering. Besides recovering the known results for bulk normal metals and BCS superconductors, we consider two experimentally relevant geometries of superconductor-normal metal proximity contacts. Both structures feature a significantly suppressed cooling power at low temperatures related to the existence of a minigap in the quasiparticle spectrum. This improved isolation low cooling feature in combination with the high tunability makes such structures highly promising candidates for quantum calorimetry