# Coupling and braiding Majorana bound states in networks defined in proximitized two-dimensional electron gases

## TL;DR

This paper predicts and analyzes the controllable coupling of Majorana bound states in 2D electron gas platforms with superconducting layers, demonstrating potential for scalable quantum computing through gate-tunable braiding operations.

## Contribution

It introduces two realistic designs for Majorana networks in 2D electron gases and demonstrates their tunable coupling and braiding feasibility through numerical simulations.

## Key findings

- Majorana bound states can be realized with achievable parameters.
- MBS coupling can be tuned from <1 neV to >10 μeV using gates.
- Braiding operations are feasible within 10-100 ns.

## Abstract

Two-dimensional electron gases with strong spin-orbit coupling covered by a superconducting layer offer a flexible and potentially scalable platform for Majorana networks. We predict Majorana bound states (MBSs) to appear for experimentally achievable parameters and realistic gate potentials in two designs: either underneath a narrow stripe of a superconducting layer (S-stripes) or where a narrow stripe has been removed from a uniform layer (N-stripes). The coupling of the MBSs can be tuned for both types in a wide range (< 1 neV to >10 $\mu$eV) using gates placed adjacent to the stripes. For both types, we numerically compute the local density of states for two parallel Majorana-stripe ends as well as Majorana trijunctions formed in a tuning-fork geometry. The MBS coupling between parallel Majorana stripes can be suppressed below 1 neV for potential barriers in the meV range for separations of about 200 nm. We further show that the MBS couplings in a trijunction can be gate-controlled in a range similar to the intra-stripe coupling while maintaining a sizable gap to the excited states (tens of $\mu$eV). Altogether, this suggests that braiding can carried out on a time scale of 10-100 ns.