Quasiparticle dynamics in ballistic weak links under weak voltage bias: An elementary treatment

TL;DR

This paper presents a simple one-dimensional model for ballistic SNS weak links under weak voltage bias, explaining quasiparticle dynamics, phase coherence, and the origin of half-voltage Shapiro steps with minimal assumptions.

Contribution

It introduces an adiabatic perturbation theory approach to describe quasiparticle behavior in ballistic SNS weak links, linking phase dynamics to observable Shapiro steps.

Findings

Quasiparticle wave functions retain phase information during transitions.

The model naturally explains the appearance of half-voltage Shapiro steps.

Weak temperature dependence of these steps is accounted for.

Abstract

A simple one-dimensional model for SNS weak links in the ballistic limit is presented. In the presence of a bias voltage, the quasiparticle state at any given instant of time is described as a superposition of that particular set of phase-dependent Andreev bound states that belongs to the specific phase difference present at this instant between the superconducting banks. The treatment -- basically a form of adiabatic perturbation theory -- has a strong formal similarity to the treatment of the k-space dynamics of an electron in a periodic potential under perturbation by an external electric field, sufficiently strong to cause transitions across the energy gaps between bands (Zener tunneling). It is shown that the quasiparticle wave function retains its phase information during analogous transitions between Andreev bands. The experimental observation of Shapiro steps at one-half the canonical voltage follows naturally from the model, along with some of the experimental properties of these steps, especially their much weaker temperature dependence, compared to the canonical steps.