Supersymmetry in the Majorana Cooper-Pair Box

TL;DR

This paper demonstrates that a Majorana Cooper-pair box with a 4pi-periodic Josephson coupling exhibits a hidden supersymmetry, leading to energy level degeneracies that can be experimentally observed, linking supersymmetry to condensed matter systems.

Contribution

It introduces a natural realization of supersymmetry in a condensed matter system through a Majorana Josephson junction, extending the understanding of supersymmetric quantum mechanics.

Findings

Energy level degeneracy due to supersymmetry can be observed in tunneling experiments.

The supersymmetry relies on the presence of an anomalous Josephson junction.

Degeneracy signatures provide evidence for Majorana modes in superconducting systems.

Abstract

Over the years, supersymmetric quantum mechanics has evolved from a toy model of high energy physics to a field of its own. Although various examples of supersymmetric quantum mechanics have been found, systems that have a natural realization are scarce. Here, we show that the extension of the conventional Cooper-pair box by a 4pi-periodic Majorana-Josephson coupling realizes supersymmetry for certain values of the ratio between the conventional Josephson and the Majorana- Josephson coupling strength. The supersymmetry we find is a "hidden" minimally bosonized supersymmetry that provides a non-trivial generalization of the supersymmetry of the free particle and relies crucially on the presence of an anomalous Josephson junction in the system. We show that the resulting degeneracy of the energy levels can be probed directly in a tunneling experiment and discuss the various transport signatures. An observation of the predicted level degeneracy would provide clear evidence for the presence of the anomalous Josephson coupling.