Josephson effect in topological superconducting rings coupled to a microwave cavity

TL;DR

This paper theoretically investigates the Josephson effect in topological superconducting rings coupled to a microwave cavity, revealing distinctive flux periodicities and the influence of Majorana modes on cavity response.

Contribution

It introduces a comprehensive model that captures the interplay between Majorana modes and bulk states, elucidating the transition from topological to trivial phases in superconducting rings.

Findings

Cavity response shows 4π periodicity in the topological phase due to Majorana fermions.

Response is 2π periodic in the non-topological phase, consistent with normal Josephson effect.

The cavity signal strongly depends on cavity frequency and ground state parity.

Abstract

We theoretically study a one dimensional p-wave superconducting mesoscopic ring interrupted by a weak link and coupled inductively to a microwave cavity. We establish an input-output description for the cavity field in the presence of the ring, and identify the electronic contributions to the cavity response and their dependence on various parameters, such as the magnetic flux, chemical potential, and cavity frequency. We show that the cavity response is $4\pi$ periodic as a function of the magnetic flux in the topological region, stemming from the so called fractional Josephson current carried by the Majorana fermions, while it is $2\pi$ periodic in the non-topological phase, consistent with the normal Josephson effect. We find a strong dependence of the signal on the cavity frequency, as well as on the parity of the ground state. Our model takes into account fully the interplay between the low-energy Majorana modes and the gaped bulks states, which we show is crucial for visualizing the evolution of the Josephson effect during the transition from the topological to the trivial phase.