Quantum Waveguide Theory of the Josephson effect in Multiband Superconductors

TL;DR

This paper develops a quantum waveguide theory for the Josephson effect in multiband superconductors, revealing how different order parameter symmetries influence Josephson current behavior and potential experimental signatures.

Contribution

It generalizes the Josephson effect theory to multiband superconductors, providing explicit formulas and analyzing the impact of order parameter symmetries on Josephson phenomena.

Findings

$s_ ext{±}$ symmetry supports $ ext{π}$ states, absent in $s_{++}$.

Josephson current shows fragility against phase fluctuations in $s_{++}$.

Temperature dependence of critical current violates Ambegaokar-Baratoff relation.

Abstract

We formulate a quantum waveguide theory of the Josephson effect in multiband superconductors, with special emphasis on iron-based materials. By generalizing the boundary conditions of the scattering problem, we first determine the Andreev levels spectrum and then derive an explicit expression for the Josephson current which generalizes the formula of the single band case. In deriving the results, we provide a second quantization field theory allowing to evaluate the current-phase relation and the Josephson current fluctuations in multiband systems. We present results for two different order parameter symmetries,namely $s_\pm$ and $s_{++}$, which are relevant in multiband systems. The obtained results show that the $s_\pm$ symmetry can support $\pi$ states which are absent in the $s_{++}$ case. We also argue a certain fragility of the Josephson current against phase fluctuations in the $s_{++}$ case. The temperature dependence of the Josephson critical current is also analyzed and we find, for both the order parameter symmetries, remarkable violations of the Ambegaokar-Baratoff relation. The results are relevant in view of possible experiments aimed at investigating the order parameter symmetry of multiband superconductors using mesoscopic Josephson junctions.