SNS Junctions along the BCS-BEC Crossover

TL;DR

This paper develops a theoretical model for SNS junctions across the BCS-BEC crossover, analyzing how the Josephson current varies with chemical potential, temperature, and the presence of Andreev levels, revealing a shift in maximum current towards the BEC side at finite temperature.

Contribution

It introduces a comprehensive theory of SNS junctions along the BCS-BEC crossover, highlighting the behavior of Andreev levels and Josephson current in different regimes and temperatures.

Findings

Andreev levels exist in the BEC regime with sufficient normal region density of states.

Josephson current peaks on the BCS side at zero temperature, but shifts to the BEC side at finite temperature.

Maximum Josephson current occurs at the BCS-BEC crossover due to changes in Andreev level occupancy.

Abstract

We present a theory of SNS junctions, a normal metal sandwiched between two superconductors, along the crossover from the BCS to the BEC regime. We calculate the Josephson current as a function of the chemical potential relative to the band edge in the superconducting region, $\mu_S$, where the BEC phase is indicated by $\mu_S <0$. The chemical potential relative to the band edge in the normal metal, $\mu_N$, allows us to tune the junction between the SNS case ($\mu_N>0$) and the SIS case, where the superconductors are separated by a tunneling barrier. We find that there are Andreev levels in the BEC regime, as long as there is sufficient density of states in the normal region, i.e. when $\mu_N>\Delta$, where $\Delta$ is the amplitude of the superconducting order parameter. For 1D SNS junctions, we find the Josephson current $I_S$ carried by these Andreev levels to be a function of the ratio $\Delta/\Delta_d$, where $\Delta_d$ is the Andreev level spacing. At zero temperature, the Josephson current has a maximum on the BCS side of the transition where $\Delta$ is maximal. At finite temperature, however, we find that the maximum moves to the BEC side of the crossover. We identify the mechanism for this phenomenon to be the decrease in the number of Andreev levels at the BCS-BEC crossover, accompanied by an increase in excitation energy to the unoccupied levels, making it less likely that these states are thermally occupied. Thereby, at finite temperature, the Josephson current is more strongly reduced on the BCS side of the crossover, resulting in a maximal Josephson current at the BCS-BEC crossover.