Design of a Majorana trijunction

TL;DR

This paper presents the design and simulation of a Majorana trijunction device in a 2D electron gas, optimizing control parameters to enable braiding of Majorana states without closing the topological gap.

Contribution

It introduces an optimization-based approach to identify operational regimes for Majorana braiding in a trijunction device, considering disorder and device shape effects.

Findings

Successful simulation of braiding without gap closing

Identification of optimal voltage regimes for operation

Feasibility analysis under different disorder conditions

Abstract

Braiding of Majorana states demonstrates their non-Abelian exchange statistics. One implementation of braiding requires control of the pairwise couplings between all Majorana states in a trijunction device. To have adiabaticity, a trijunction device requires the desired pair coupling to be sufficiently large and the undesired couplings to vanish. In this work, we design and simulate a trijunction device in a two-dimensional electron gas with a focus on the normal region that connects three Majorana states. We use an optimisation approach to find the operational regime of the device in a multi-dimensional voltage space. Using the optimization results, we simulate a braiding experiment by adiabatically coupling different pairs of Majorana states without closing the topological gap. We then evaluate the feasibility of braiding in a trijunction device for different shapes and disorder strengths.