Non-Abelian braiding of Dirac fermionic modes in topological systems and spin superconductors

报告题目:Non-Abelian braiding of Dirac fermionic modes in topological systems and spin superconductors

报告人:吴宜家   北京大学物理学院量子材料科学中心



报告摘要:  The reason why Majorana zero-modes support non-Abelian braiding can be summarized as two conditions as: (i) ground state degeneracy, and (ii) geometric phase of π during the braiding operation. In this talk, I will present that both these two requirements can be satisfied in non-Majorana systems. As a prototyping model, the topological Dirac fermionic modes bound to the half-vortex in the quantum anomalous Hall insulator can be proved to obey non-Abelian braiding statistics. Such a vortex-bounded Dirac fermioinic mode is topologically equivalent to the Jackiw-Rebbi zero-mode in one-dimensional topological insulator and the topological corner state in higher-order topological insulator. Furthermore, the topological edge states in spin superconductor carrying half-spin also exhibit non-Abelian statistics due to the Aharonov-Casher effect, which is in parallel with the Aharonov-Bohm effect of the Majorana zero-mode possessing half-charge. All these proposals open up a new avenue realizing non-Abelian braiding without the assistance of Majorana zero-mode and charge superconductor.


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