Probing non-Abelian statistics with Majorana fermion interferometry in spin-orbit-coupled semiconductors

TL;DR

This paper demonstrates that charge current can be supported at interfaces of chiral Majorana edges in spin-orbit-coupled semiconductors, enabling electrically controlled interferometry to probe non-Abelian statistics for topological quantum computing.

Contribution

It shows that charge current at Majorana interfaces allows for electrically controlled interferometry in semiconductors, advancing the experimental approach to non-Abelian braiding.

Findings

Charge current can be supported at Majorana interfaces in semiconductors.

Electrically controlled interferometry is feasible in these systems.

This method can directly establish non-Abelian braiding statistics.

Abstract

The list of quantum mechanical systems with non-Abelian statistics has recently been expanded by including generic spin-orbit-coupled semiconductors e.g., InAs) in proximity to a s-wave superconductor. Demonstration of the anyonic statistics using Majorana fermion interferometry in this system is a necessary first step towards topological quantum computation (TQC). However, since all isolated chiral edges that can be created in the semiconductor are charge neutral, it is not clear if electrically controlled interferometry is possible in this system. Here we show that when two isolated chiral Majorana edges are brought into close contact, the resultant interface supports charge current, enabling electrically controlled Majorana fermion interferometry in the semiconductor structure. Such interferometry experiments on the semiconductor are analogous to similar interferometry experiments on the $\nu=5/2$ fractional quantum Hall systems and on the surface of a 3D strong topological insulator, illustrating the usefulness of the 2D semiconductor heterostructure as a suitable TQC platform. In particular, we proposed Majorana interferometers may be the most direct method for establishing non-Abelian braiding statistics in topological superconductors.