Josephson transport through a Hubbard impurity center

TL;DR

This paper studies how impurity centers with Hubbard interactions affect Josephson current in superconducting junctions, revealing sign changes and fluctuations depending on interaction type and impurity energy levels.

Contribution

It introduces a model for Josephson transport through Hubbard impurities, analyzing effects of both repulsive and attractive interactions on current behavior.

Findings

Josephson current sign changes with temperature for repulsive interactions within specific energy ranges.

Prediction of strong temporal fluctuations of current with few impurity centers.

Reduction to a two-level system for attractive interactions at low temperatures.

Abstract

We investigate the Josephson transport through a thin semiconductor barrier containing impurity centers with the on-site Hubbard interaction $u$ of an arbitrary sign and strength. We find that in the case of the repulsive interaction the Josephson current changes sign with the temperature increase if the energy of the impurity level $\epsilon$ (measured from the Fermi energy of superconductors) falls in the interval $(-u,0)$. We predict strong temporal fluctuations of the current if only a few centers present within the junction. In the case of the attractive impurity potential ($u<0$) and at low temperatures, the model is reduced to the effective two level Hamiltonian allowing thus a simple description of the nonstationary Josephson effect in terms of pair tunneling processes.