Majorana fermion from Landau quantization in 2D topological superconductors

TL;DR

This paper explores how magnetic fields in 2D topological superconductors can generate and control Majorana fermions, which are promising for quantum computing applications.

Contribution

It demonstrates that a single vortex can host two Majorana fermions and shows how magnetic fields can tune their coupling in 2D topological superconductor systems.

Findings

A vortex hosts two Majorana fermions, one at the core.

The second Majorana's wave function is localized along a circle with radius inversely proportional to B.

Magnetic field control can tune Majorana fermion coupling.

Abstract

We study the generation of Majorana fermions in a two-dimensional topological superconductor placed in a transverse magnetic field B. A topological insulator/superconductor heterostructure and a two-dimensional p-wave superconductor are discussed. It is demonstrated that in these systems a single vortex creates two Majorana fermions, one hosted at the vortex core. The wave function of the second Majorana state is localized in the superconductor volume along a circle of radius $r^* \propto B^{-1}$ centered at the vortex core. In the case of many vortices, the sensitivity of $r^*$ to the magnetic field B may be used to control the coupling between the Majorana fermions. The latter property could be an asset for quantum computations.