Josephson effect for superconductors lacking center of inversion

TL;DR

This paper explores how the absence of inversion symmetry in certain superconductors leads to an anomalous Josephson effect, especially when time-reversal symmetry is also broken, with implications for cuprates and heavy-fermion materials.

Contribution

It demonstrates the existence of an anomalous Josephson current caused by mixed p-wave and d-wave order parameters in non-centrosymmetric superconductors with broken time-reversal symmetry.

Findings

Anomalous Josephson current occurs along the p-wave axis.

The effect involves Meissner and loop currents at the tunnel barrier.

Relevance to cuprates and heavy-fermion compounds with broken symmetries.

Abstract

Due to the absence of a center of inversion in some superconducting compounds, a p-wave admixture to the dominant d-wave order parameter must exist. If time-reversal is also violated, an allowed invariant is the product of the d-wave, p-wave and an appropriately directed current. We show that this leads to an anomalous Josephson current for tunneling along the direction parallel to the axis of the p-wave component, where the current is the Meissner current and the Josephson loop current along the surface of the tunnel barrier. These ideas are applied to the superconducting state of the cuprates in the pseudogap region of the phase diagram where in the normal phase some experiments have detected a time-reversal and inversion symmetry broken phase. The effect is relevant also to heavy-fermion compounds which lack center of inversion due to crystalline symmetry.