Non-Abelian operation through scattering between chiral Dirac edge modes

TL;DR

This paper proposes a theoretical method to realize non-Abelian braiding operations using scattering between chiral Dirac edge modes in quantum anomalous Hall insulators, with potential applications in topologically protected quantum computing.

Contribution

It introduces an analytical model and device proposal for non-Abelian braiding via CDEMs, and verifies properties through numerical tunneling conductance analysis.

Findings

Analytical derivation of the S-matrix for CDEM scattering.

Proposal of a device for experimental realization of non-Abelian braiding.

Numerical verification of non-Abelian properties through tunneling conductance simulations.

Abstract

We theoretically demonstrate that non-Abelian braiding operation can be realized through the scattering between chiral Dirac edge modes (CDEMs) in quantum anomalous Hall insulators by analytically deriving its S-matrix. Based on the analytical model, we propose a viable device for the experimental realization and detection of the non-Abelian braiding operations. Through investigating the tunneling conductance in a discretized lattice model, the non-Abelian properties of CDEMs could also be verified in a numerical way. Our proposal for the CDEM-based braiding provides a new avenue for realizing topologically protected quantum gates.