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 form...
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Online Access: | http://dx.doi.org/10.5488/CMP.19.33703 |
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doaj-5e51ad9357ee417886c2a8432da3c0a82020-11-24T20:45:38ZengInstitute for Condensed Matter PhysicsCondensed Matter Physics1607-324X2016-09-011933370310.5488/CMP.19.33703Counting Majorana bound states using complex momentaI. MandalRecently, 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.http://dx.doi.org/10.5488/CMP.19.33703exceptional pointsMajorana fermionsBDIDIIIDcounting |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
I. Mandal |
spellingShingle |
I. Mandal Counting Majorana bound states using complex momenta Condensed Matter Physics exceptional points Majorana fermions BDI DIII D counting |
author_facet |
I. Mandal |
author_sort |
I. Mandal |
title |
Counting Majorana bound states using complex momenta |
title_short |
Counting Majorana bound states using complex momenta |
title_full |
Counting Majorana bound states using complex momenta |
title_fullStr |
Counting Majorana bound states using complex momenta |
title_full_unstemmed |
Counting Majorana bound states using complex momenta |
title_sort |
counting majorana bound states using complex momenta |
publisher |
Institute for Condensed Matter Physics |
series |
Condensed Matter Physics |
issn |
1607-324X |
publishDate |
2016-09-01 |
description |
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. |
topic |
exceptional points Majorana fermions BDI DIII D counting |
url |
http://dx.doi.org/10.5488/CMP.19.33703 |
work_keys_str_mv |
AT imandal countingmajoranaboundstatesusingcomplexmomenta |
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1716814301440770048 |