Majorana bound state of a Bogoliubov-de Gennes-Dirac Hamiltonian in arbitrary dimensions |
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Authors: | Ken-Ichiro Imura Takahiro FukuiTakanori Fujiwara |
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Institution: | a Department of Quantum Matter, AdSM, Hiroshima University, 739-8530, Japan b Department of Physics, Ibaraki University, Mito 310-8512, Japan |
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Abstract: | We study a Majorana zero-energy state bound to a hedgehog-like point defect in a topological superconductor described by a Bogoliubov-de Gennes (BdG)-Dirac type effective Hamiltonian. We first give an explicit wave function of a Majorana state by solving the BdG equation directly, from which an analytical index can be obtained. Next, by calculating the corresponding topological index, we show a precise equivalence between both indices to confirm the index theorem. Finally, we apply this observation to reexamine the role of another topological invariant, i.e., the Chern number associated with the Berry curvature proposed in the study of protected zero modes along the lines of topological classification of insulators and superconductors. We show that the Chern number is equivalent to the topological index, implying that it indeed reflects the number of zero-energy states. Our theoretical model belongs to the BDI class from the viewpoint of symmetry, whereas the spatial dimension d of the system is left arbitrary throughout the paper. |
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Keywords: | Majorana bound state Bogoliubov-de Gennes equation Dirac Hamiltonian Index theorem Topological invariant Berry phase |
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