Braiding Induced by Finite-Size Effect in One-Dimensional Topological Superconductors

TL;DR

This paper proposes a method to braid Majorana zero modes and Majorana Kramers pairs in one-dimensional topological superconductors using finite-size effects and tunable couplings, advancing topological quantum computing.

Contribution

It introduces an effective model for braiding MZMs and MKPs in 1D topological superconductors, enabling state initialization and readout via gate control.

Findings

Demonstrates braiding of MZMs and MKPs using finite-size effects.

Provides a scheme for state initialization and readout.

Suggests experimental verification of non-Abelian statistics.

Abstract

We investigate the transport properties of Majorana zero mode (MZM) and Majorana Kramers pair (MKP) in one-dimensional topological superconductors, respectively. An effective model is established for braiding of MZMs and MKPs. We employ the $d_{x^{2}-y^{2}}$-wave topological superconductors to embody the effective model for braiding of MKPs by utilizing finite-size effects and locally tunable coupling parameters. We show how to construct the state initialization and readout via gate control. We also use this method for braiding MZMs in s-wave topological superconductors. Our proposal presents a promising avenue for experimentally verifying the non-Abelian statistical properties of MZMs and MKPs, with implications for topological quantum computing.