Physics – Condensed Matter – Superconductivity
Scientific paper
2011-07-28
Nuclear Physics B854:306-320, 2012
Physics
Condensed Matter
Superconductivity
12 pages
Scientific paper
10.1016/j.nuclphysb.2011.09.003
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 of the system is left arbitrary throughout the paper.
Fujiwara Takanori
Fukui Takahiro
Imura Ken-ichiro
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