Phase diffusion and fractional Shapiro steps in superconducting quantum point contacts

TL;DR

This paper investigates how classical phase diffusion affects fractional Shapiro steps in superconducting quantum point contacts, revealing temperature's stronger impact on fractional steps and extending analysis to complex environments.

Contribution

It introduces a detailed analysis of phase diffusion effects on fractional Shapiro steps, including analytical solutions and environmental extensions.

Findings

Temperature has a stronger effect on fractional than integer steps.

Numerical solutions provide phase difference probability densities.

Extended models include two resistances and finite capacitance.

Abstract

We study the influence of classical phase diffusion on the fractional Shapiro steps in resistively shunted superconducting quantum point contacts. The problem is mapped onto a Smoluchowski equation with a time dependent potential. A numerical solution for the probability density of the phase difference between the leads gives access to the mean current and the mean voltage across the contact. Analytical solutions are derived in some limiting cases. We find that the effect of temperature is stronger on fractional than on integer steps, in accordance with preliminary experimental findings. We further extend the analysis to a more general environment including two resistances and a finite capacitance.