Majorana fermion exchange in quasi-one-dimensional networks

TL;DR

This paper investigates how the local properties of junctions in Majorana wire networks influence non-Abelian statistics, impacting the design of topological quantum computing platforms.

Contribution

It demonstrates that junction chirality variations affect Majorana exchange statistics, highlighting the importance of local junction properties in network-based TQC.

Findings

Junction chirality determines non-Abelian exchange behavior.

Chirality consistency is not required across the network.

Experimental methods to compare junction chiralities are discussed.

Abstract

Heterostructures of spin-orbit coupled materials with s-wave superconductors are thought to be capable of supporting zero-energy Majorana bound states. Such excitations are known to obey non-Abelian statistics in two dimensions, and are thus relevant to topological quantum computation (TQC). In a one-dimensional system, Majorana states are localized to phase boundaries. In order to bypass the constraints of one-dimension, a wire network may be created, allowing the exchange of Majoranas by way of junctions in the network. Alicea et al. have proposed such a network as a platform for TQC, showing that the Majorana bound states obey non-Abelian exchange statistics even in quasi-one-dimensional systems. Here we show that the particular realization of non- Abelian statistics produced in a Majorana wire network is highly dependent on the local properties of individual wire junctions. For a simply connected network, the possible realizations can be characterized by the chirality of individual junctions. There is in general no requirement for junction chiralities to remain consistent across a wire network. We show how the chiralities of different junctions may be compared experimentally and discuss the implications for TQC in Majorana wire networks.