Counting Majorana bound states using complex momenta
Recently, the connection between Majorana fermions bound to the defects in arbitrary dimensions, and complex momentum roots of the vanishing determinant of the corresponding bulk Bogoliubov–de Gennes (BdG) Hamiltonian, has been established (EPL, 2015, 110, 67005). Based on this understanding, a for...
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| Date: | 2016 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут фізики конденсованих систем НАН України
2016
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| Series: | Condensed Matter Physics |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/156221 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Counting Majorana bound states using complex momenta / I. Mandal // Condensed Matter Physics. — 2016. — Т. 19, № 3. — С. 33703: 1–21. — Бібліогр.: 56 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | Recently, the connection between Majorana fermions bound to the defects in arbitrary dimensions, and complex momentum roots of the vanishing determinant of the corresponding bulk Bogoliubov–de Gennes (BdG)
Hamiltonian, has been established (EPL, 2015, 110, 67005). Based on this understanding, a formula has been
proposed to count the number (n) of the zero energy Majorana bound states, which is related to the topological
phase of the system. In this paper, we provide a proof of the counting formula and we apply this formula to a
variety of 1d and 2d models belonging to the classes BDI, DIII and D. We show that we can successfully chart out
the topological phase diagrams. Studying these examples also enables us to explicitly observe the correspondence between these complex momentum solutions in the Fourier space, and the localized Majorana fermion
wavefunctions in the position space. Finally, we corroborate the fact that for systems with a chiral symmetry, these solutions are the so-called “exceptional points”, where two or more eigenvalues of the complexified
Hamiltonian coalesce. |
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