Anomalous Josephson current, incipient time-reversal symmetry breaking, and Majorana bound states in interacting multi-level dots

TL;DR

This paper investigates how spin-orbit interaction, magnetic field, and Coulomb interactions influence the Josephson current in multi-level quantum dots, revealing conditions for anomalous supercurrent and Majorana states.

Contribution

It provides a comprehensive model analyzing the interplay of interactions and spin effects in quantum dots, identifying conditions for anomalous currents and Majorana bound states.

Findings

Finite anomalous supercurrent I_a can occur with weak Zeeman fields and interactions.

Incipient spontaneous time-reversal symmetry breaking is observed.

Conditions for realizing Majorana bound states are established.

Abstract

We study the combined effects of spin-orbit interaction, magnetic field, and Coulomb charging on the Josephson current-phase relation, I(\varphi), for a multi-level quantum dot tunnel-contacted by two conventional s-wave superconductors with phase difference \varphi. A general model is formulated and analyzed in the cotunneling regime (weak tunnel coupling) and in the deep subgap limit, fully taking into account interaction effects. We determine the conditions for observing a finite anomalous supercurrent I_a=I(\varphi=0). For a two-level dot with spin-orbit coupling and arbitrarily weak Zeeman field B, we find the onset behavior I_a\propto {\rm sgn}(B) in the presence of interactions, suggesting the incipient spontaneous breakdown of time-reversal symmetry. We also provide conditions for realizing spatially separated (but topologically unprotected) Majorana bound states in this system, which have a clear signature in the 2\pi-periodic current-phase relation.