Quasiparticle relaxation in superconducting nanostructures

TL;DR

This paper investigates how non-equilibrium quasiparticles relax energy in dirty superconductors, emphasizing phonon emission, the influence of magnetic fields, and quasiparticle trapping mechanisms in nanostructures.

Contribution

It develops a theoretical framework for quasiparticle relaxation rates considering broken time reversal symmetry and explores quasiparticle trapping beyond the coherence length.

Findings

Relaxation dominated by phonon emission in dirty superconductors.

Magnetic fields significantly affect quasiparticle relaxation rates.

Quasiparticle trapping can occur at distances much larger than the coherence length.

Abstract

We examine energy relaxation of non-equilibrium quasiparticles in "dirty" superconductors with the electron mean free path much shorter than the superconducting coherence length. Relaxation of low-energy non-equilibrium quasiparticles is dominated by phonon emission. We derive the corresponding collision integral and find the quasiparticle relaxation rate. The latter is sensitive to the breaking of time reversal symmetry (TRS) by a magnetic field (or magnetic impurities). As a concrete application of the developed theory, we address quasiparticle trapping by a vortex and a current-biased constriction. We show that trapping of hot quasiparticles may predominantly occur at distances from the vortex core, or the constriction, significantly exceeding the superconducting coherence length.