Superconducting triangular islands as a platform for manipulating Majorana zero modes

TL;DR

This paper proposes using superconducting triangular islands to host and manipulate Majorana zero modes, offering a potentially more feasible platform for topological quantum computation compared to wire-based architectures.

Contribution

It introduces a new approach to realize and control Majorana zero modes at the corners of superconducting triangles, including minimal models and practical structures like hollow triangles with supercurrents.

Findings

MZM can appear at triangle vertices controlled by vector potentials.

Hollow triangles with different topological phases can host MZM.

Feasibility of constructing such triangles with existing systems is discussed.

Abstract

Current proposals for topological quantum computation (TQC) based on Majorana zero modes (MZM) have mostly been focused on coupled-wire architecture which can be challenging to implement experimentally. To explore alternative building blocks of TQC, in this work we study the possibility of obtaining robust MZM at the corners of triangular superconducting islands, which often appear spontaneously in epitaxial growth. We first show that a minimal three-site triangle model of spinless $p$-wave superconductor allows MZM to appear at different pairs of vertices controlled by a staggered vector potential, which may be realized using coupled quantum dots and can already demonstrate braiding. For systems with less fine-tuned parameters, we suggest an alternative structure of a "hollow" triangle subject to uniform supercurrents or vector potentials, in which MZM generally appear when two of the edges are in a different topological phase from the third. We also discuss the feasibility of constructing the triangles using existing candidate MZM systems and of braiding more MZM in networks of such triangles.