Dissipative conductivity of a dirty superconductor with Dynes subgap states under a dc bias current up to the depairing current density

TL;DR

This paper investigates how Dynes subgap states and dc bias influence the dissipative conductivity of dirty superconductors, revealing ways to optimize supercurrent and reduce dissipation in quantum devices.

Contribution

It provides a detailed analysis of the effects of Dynes parameter and dc bias on superconductor properties, offering strategies to enhance supercurrent and minimize dissipation.

Findings

Finite Dynes parameter reduces superfluid density and depairing current density.

Broadening of quasiparticle density of states can lower dissipative conductivity.

Optimal combination of Dynes parameter and bias minimizes dissipation.

Abstract

We study the dissipative conductivity $\sigma_1$ of a dirty superconductor with a finite Dynes parameter $\Gamma$ under a dc-biased weak time-dependent field. The Usadel equation for the current-carrying state is solved to calculate the pair potential, penetration depth, supercurrent density, and quasiparticle spectrum. It is shown that, while the depairing current density $j_d$ for $\Gamma=0$ is coincident with the Kupriyanov-Lukichev theory, a finite $\Gamma$ decreases the superfluid density, resulting in a reduction of $j_d$. The broadening of the peaks of the quasiparticle density of states induced by a combination of a finite $\Gamma$ and a dc bias can reduce $\sigma_1$ below that for the ideal dirty BCS superconductor with $\Gamma=0$, while subgap states at Fermi level proportional to $\Gamma$ results in a residual conductivity at $T\to 0$. We find the optimum combination of $\Gamma$ and the dc bias to minimize $\sigma_1$ by scanning all $\Gamma$ and all currents up to $j_d$. By using the results, it is possible to improve $j_d$ and reduce electromagnetic dissipation in various superconducting quantum devices.