Controlling non-Abelian statistics of Majorana fermions on Majorana dimer lattices

TL;DR

This paper proposes a controllable method to exchange Majorana fermions in topological superconducting wires using tunneling, enabling verification of their non-Abelian statistics despite the one-dimensional topology constraints.

Contribution

It introduces a tunneling-based scheme to manipulate Majorana fermions across wires, facilitating the study of their non-Abelian exchange properties.

Findings

Tunneling can be controlled by gate voltages to move Majorana fermions.

The exchange process is described by a non-Abelian braid operator.

The scheme enables verification of Majorana non-Abelian statistics.

Abstract

Under appropriate external conditions a semiconductor nanowire in proximity to an s-wave superconductor can be in a topological superconducting (TS) phase. This phase supports localized zero-energy Majorana fermions at the ends of the wire. However, the non-Abelian exchange statistics of Majorana fermions is difficult verify because of the one-dimensional topology of such wires. In this paper we propose a scheme to transport Majorana fermions between the ends of different wires using tunneling, which is shown to be controllable by gate voltages. Such tunneling-generated hops of Majorana fermions can be used to exchange the Majorana fermions. The exchange process thus obtained is described by a non-Abelian braid operator that is uniquely determined by the well-controlled microscopic tunneling parameters.