Josephson and persistent currents in a quantum ring between topological superconductors

TL;DR

This paper studies the energy spectra and current behaviors in a quantum ring Josephson junction between topological superconductors hosting Majorana states, revealing topologically protected spectral patterns that influence observable currents.

Contribution

It introduces a detailed numerical analysis of spectra in a topological Josephson junction, highlighting spectral patterns and their relation to persistent and Josephson currents.

Findings

Spectra exhibit line, point, and undulated node patterns.

Topologically protected flat bands are identified.

Spectral patterns influence measurable current signals.

Abstract

In this work, we investigate the spectra in an Aharonov-Bohm quantum-ring interferometer forming a Josephson junction between two topological superconductors (TSC) nanowires. The TSCs host Majorana bound states at their edges, and both the magnetic flux and the superconducting phase difference between the TSCs are used as control parameters. We use a tight-binding approach to model the quantum ring coupled to both TSCs, described by the Kitaev effective Hamiltonian. We solve the problem by means of exact numerical diagonalization of the Bogoliubov-de Gennes (BdG) Hamiltonian and obtain the spectra for two sizes of the quantum ring as a function of the magnetic flux and the phase difference between the TSCs. Depending on the size of the quantum ring and the coupling, the spectra display several patterns. Those are denoted as line, point and undulated nodes, together with flat bands, which are topologically protected. The first three patterns can be possibly detected by means of persistent and Josephson currents. Hence, our results could be useful to understand the spectra and their relation with the behavior of the current signals.