Non-Abelian braiding of Dirac fermionic modes using topological corner states in higher-order topological insulator

TL;DR

This paper demonstrates that topological corner states in higher-order topological insulators exhibit non-Abelian braiding, extending the concept beyond Majorana modes, with analytical and experimental proposals for verification.

Contribution

It shows that Dirac fermionic modes in higher-order topological insulators can support non-Abelian braiding, providing analytical descriptions and experimental test proposals.

Findings

Topological corner states possess non-Abelian braiding properties.

Dirac fermionic modes support non-Abelian braiding, similar to Majorana modes.

Experimental setup using topological electric circuits is proposed.

Abstract

We numerically demonstrate that the topological corner states residing in the corners of higher-order topological insulator possess non-Abelian braiding properties. Such topological corner states are Dirac fermionic modes other than Majorana zero-modes. We claim that Dirac fermionic modes protected by nontrivial topology also support non-Abelian braiding. An analytical description on such non-Abelian braiding is conducted based on the vortex-induced Dirac-type fermionic modes. The braiding operator for Dirac fermionic modes is also analytically derivated and compared with the Majorana zero-modes. Experimentally, such non-Abelian braiding operation on Dirac fermionic modes is proposed to be testified through topological electric circuit.