Majorana fermions at the edge of superconducting islands

TL;DR

This paper studies the emergence and stability of Majorana fermions at the edges of superconducting islands on topological insulators, highlighting conditions for their robustness and experimental distinguishability.

Contribution

It provides a detailed analysis of Majorana fermions localized at the edges of superconducting islands, including their robustness and experimental signatures.

Findings

Majorana fermions appear at the edge if an odd number of vortices is present.

The energy gap can be comparable to the induced superconducting gap.

Edge Majorana fermions can be distinguished from Dirac fermions via their stability and response to external parameters.

Abstract

We investigate the properties of electron states localized at the edge of a superconducting island placed on the surface of a topological insulator in a magnetic field. In such systems, Majorana fermions emerge if an odd number of vortices (or odd multivortex vorticity) is hosted by the island; otherwise, no Majorana states exist. Majorana states emerge in pairs: one state is localized near the vortex core, and another at the island edge. We analyze in detail the robustness of Majorana fermions at the edge of the island threaded by a single vortex. If the system parameters are optimized, the energy gap between the Majorana fermion and the first excited state at the edge is of the order of the superconducting gap induced on the surface of the topological insulator. The stability of the Majorana fermion state against a variation of the gate voltage and its sensitivity to the magnetic field allows one to distinguish experimentally the edge Majorana fermion from conventional Dirac fermions.