Majorana bound state of a Bogoliubov-de Gennes-Dirac Hamiltonian in arbitrary dimensions
Nuclear Physics B Volume 854 Issue 2
Page 306-320
published_at 2012-01-11
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| File | |
| Title ( eng ) |
Majorana bound state of a Bogoliubov-de Gennes-Dirac Hamiltonian in arbitrary dimensions
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| Creator |
Fukui Takahiro
Fujiwara Takanori
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| Source Title |
Nuclear Physics B
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| Volume | 854 |
| Issue | 2 |
| Start Page | 306 |
| End Page | 320 |
| 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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| Descriptions |
This work was supported in part by Grant-in-Aid for Scientific Research from JSPS (No. 21540378) and by the “Topological Quantum Phenomena” Grant-in Aid for Scientific Research on Innovative Areas from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan (Nos. 23103502, 23103511).
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| NDC |
Physics [ 420 ]
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| Language |
eng
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| Resource Type | journal article |
| Publisher |
Elsevier B.V.
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| Date of Issued | 2012-01-11 |
| Rights |
Copyright (c) 2011 Elsevier B.V.
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| Publish Type | Author’s Original |
| Access Rights | open access |
| Source Identifier |
[ISSN] 0550-3213
[NCID] AA00760043
[DOI] 10.1016/j.nuclphysb.2011.09.003
[arXiv] arXiv:1107.5629
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