Microscopic Theory of Josephson Mesoscopic Constrictions

TL;DR

This paper develops a microscopic non-equilibrium Green function theory to analyze the Josephson effect in mesoscopic constrictions, accounting for various length scales and revealing phase oscillations and phase-slip solutions.

Contribution

It introduces a self-consistent microscopic approach for Josephson constrictions, extending analysis to regimes where key length scales are comparable.

Findings

Phase oscillations with period λ_F/2 observed when λ_F is smaller than constriction and coherence lengths.

Existence of phase-slip center solutions for constriction length greater than coherence length.

The theory aligns with previous phenomenological models for phase-slip phenomena.

Abstract

We present a microscopic theory for the d.c. Josephson effect in model mesoscopic constrictions. Our method is based on a non-equilibrium Green function formalism which allows for a self-consistent determination of the order parameter profile along the constriction. The various regimes defined by the different length scales (Fermi wavelength $\lambda_F$, coherence length $\xi_0$ and constriction length $L_C$) can be analyzed, including the case where all these lengths are comparable. For the case $\lambda_F \tilde{<} (L_C,\xi_0)$ phase oscillations with spatial period $\lambda_F/2$ can be observed. In the case of $L_C>\xi_0$ solutions with a phase-slip center inside the constriction can be found, in agreement with previous phenomenological theories.