Analytical calculation of the excess current in the OTBK theory

TL;DR

This paper derives an analytical expression for the excess current in Josephson junctions based on the OTBK theory, confirming previous numerical results and extending them to asymmetric barriers, aiding experimental data analysis.

Contribution

It provides the first analytical formulas for excess current in asymmetric Josephson junctions within the OTBK framework, facilitating better experimental data fitting.

Findings

Confirmed negative excess current at low transparencies.

Derived analytical formulas for symmetric and asymmetric barriers.

Validated formulas with previous numerical results.

Abstract

We present an analytical derivation of the excess current in Josephson junctions within the Octavio-Tinkham-Blonder-Klapwijk theory for both symmetric and asymmetric barrier strengths. We confirm the result found numerically by Flensberg et al. for equal barriers [Phys. Rev. B 38, 8707 (1988)], including the prediction of negative excess current for low transparencies, and we generalize it for differing barriers. Our analytical formulae provide for convenient fitting of experimental data, also in the less studied, but practically relevant case of the barrier asymmetry.