Out-of-equilibrium heating of electron liquid: fermionic and bosonic temperatures

TL;DR

This paper explores how electric bias and temperature gradients create distinct effective temperatures for different excitations in a disordered 2D superconductor's electron liquid, enabling control and measurement of these temperatures.

Contribution

It introduces the concept of multiple effective temperatures for various excitations in out-of-equilibrium superconductors and proposes experimental methods to measure them.

Findings

Distinct effective temperatures for single-particle, Cooper pairs, and electron-hole excitations.

Control of excitation temperatures via electric and thermal current ratios.

Proposed experimental setup for measuring these effective temperatures.

Abstract

We investigate out-of-the equilibrium properties of the electron liquid in a two-dimensional disordered superconductor subject to the electric bias and temperature gradient. We calculate kinetic coefficients and Nyquist noise, and find that they are characterized by distinct effective temperatures: $T_{\mathrm{e}}$, characterizing single-particle excitations, $T_{\mathrm{Cp}}$, describing the Cooper pairs, and $T_{\mathrm{eh}}$, corresponding to electron-hole or dipole excitations. Tuning the ratio between the electric $j$ and thermal $j_{\mathrm{th}}$ currents and the boundary conditions one can heat different kind of excitations and control their corresponding temperatures. We propose the experimental setting for determining these effective temperatures.