Non-Abelian Braiding of Dirac Fermionic Modes Using Topological Corner States in Higher-Order Topological Insulator
Yijia Wu, Hua Jiang, Jie Liu, Haiwen Liu, Xiaoming Xie
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. Finally, the braiding operators for Dirac fermionic modes, especially their explicit matrix forms, are analytically derived and compared with the case of Majorana zero modes.
Topics & Concepts
MAJORANAPhysicsTopological insulatorTopology (electrical circuits)Dirac (video compression format)Abelian groupTopological quantum numberTopological orderSymmetry protected topological orderQuantum mechanicsFermionQuantumMathematicsPure mathematicsCombinatoricsNeutrinoTopological Materials and PhenomenaQuantum Mechanics and Non-Hermitian PhysicsQuantum many-body systems