Manifestation of Majorana modes overlap in the Aharonov-Bohm effect

TL;DR

This paper investigates how the overlap of Majorana modes in topological superconducting wires affects Aharonov-Bohm oscillations, revealing a shift and period doubling linked to Majorana hybridization, supported by numerical and analytical models.

Contribution

It demonstrates the impact of Majorana mode hybridization on AB oscillations, including a fundamental phase shift and period doubling, through combined numerical and analytical analysis.

Findings

AB oscillation shift due to Majorana hybridization

Period doubling of AB oscillations observed

Fundamental {c0}/2 phase shift identified

Abstract

One of the key features of the Majorana bound states emerging in topological superconducting (SC) wires is increasing oscillations of their energy under the growth of magnetic field or chemical potential due to concomitant enhancement of hybridization of the Majorana mode wave functions initially localized at the opposite edges of the structure. In this study we found that the other consequence of it is a shift of Aharonov-Bohm (AB) oscillations of linear-response conductance in an interference device where two ends of the SC wire connected with a normal contact via non-SC wires (arms). In addition, it is accompanied by an oscillation period doubling. The numerical calculations for the spinful system are supported by the analytical results for different spinless models allowing to track the conductance evolution as the hybridization of the Majorana modes increases. It is shown that since the coupling between the different arms and normal contact is implemented only via the different-type Majoranas the AB oscillations acquire a fundamental {\pi}/2 shift in comparison with the effect for an analogous system of zero-energy quantum dots.