Majorana fermion exchange in strictly one-dimensional structures

Department of Physics and Astronomy, University of British Columbia - Vancouver, BC, Canada V6T 1Z1 and Quantum Matter Institute, University of British Columbia - Vancouver BC, Canada V6T 1Z4

Received: 14 December 2014
Accepted: 24 March 2015

Abstract

It is generally thought that the adiabatic exchange of two identical particles is impossible in one spatial dimension. Here we describe a simple protocol that permits the adiabatic exchange of two Majorana fermions in a one-dimensional topological superconductor wire. The exchange relies on the concept of “Majorana shuttle” whereby a π domain wall in the superconducting order parameter which hosts a pair of ancillary majoranas delivers one zero mode across the wire while the other one tunnels in the opposite direction. The method requires some tuning of parameters and does not, therefore, enjoy full topological protection. The resulting exchange statistics, however, remain non-Abelian for a wide range of parameters that characterize the exchange.