Logical Majorana zero modes in a nanowire network

TL;DR

This paper proposes a method to create and control logical Majorana zero modes in a nanowire network by using specially designed junctions and gate voltages, enabling the realization of topologically protected quantum states.

Contribution

It introduces a novel junction design that traps and hybridizes Majorana modes in a nanowire network to realize logical Majorana zero modes without breaking time-reversal symmetry.

Findings

Successfully traps one Majorana mode per lattice site.

Demonstrates emergence of logical Majorana zero mode at vortex core.

Identifies parameter ranges for experimental realization.

Abstract

We present a scheme to use physical Majorana quasi-zero modes at each junction of a two-dimensional nanowire network to build a logical Majorana zero mode, the location of which is controllable through gate voltages. The wire-network is a way to realize a proposal by Yang et al. arXiv:1808.04825 to imprint a Kekul\'e vortex pattern on a honeycomb lattice via gate voltages. We show that a specific type of junction -- other than a naive Y- or T-junction -- is needed to realize, without breaking time-reversal symmetry, an artificial ``graphene'' system with Majorana fermions instead of complex ones at each site. The junction we propose (i) traps exactly one physical Majorana (quasi-)zero mode at each site of either a brick wall or honeycomb lattice and (ii) allows this mode to hybridize with all three neighboring sites. Using a lattice of these junctions and starting from an electronic, tight-binding model for the wires, we imprint the voltage patterns corresponding to the Kekul\'e vortex and observe the emergence of the logical Majorana zero mode at the vortex core. We also provide the range of parameters where this excitation could be realized experimentally.