Phenomenological Model of the Nonlinear Microwave Response of a Superconductor Containing Weak Links

TL;DR

This paper introduces a phenomenological model to describe how dc and rf magnetic fields influence the microwave surface impedance of superconductors with weak links, revealing anomalous behaviors and matching experimental data.

Contribution

It presents a new phenomenological model accounting for weak links in superconductors and their nonlinear microwave response under magnetic fields.

Findings

Z_s(H) can fall below zero-field values under certain conditions

Model shows good qualitative and some quantitative agreement with experiments

Reveals anomalous dependence of surface impedance on magnetic fields

Abstract

A phenomenological model is proposed which describes the effect of both dc and rf magnetic fields, $H$, on the microwave surface impedance, Z_s=R_s+jX_s, of a superconductor containing weak link. Two cases are considered; a weak link between two grains, shunted by another grain, and a non-shunted weak link. In both cases the dependences of R_s and X_s on applied field H were found to be anomalous. Under certain conditions, the values of Z_s(H) can fall below the zero-field values. Comparison with experiment is performed, and very good qualitative and (in some cases) quantitative agreement is found.