Majoranas with and without a 'character': hybridization, braiding and chiral Majorana number
| Autor: | P. Simon, Nicholas Sedlmayr, M. Guigou, C. Bena |
|---|---|
| Přispěvatelé: | Institut de Physique Théorique - UMR CNRS 3681 (IPHT), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Physique des Solides (LPS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), European Project: 256965,NANOGRAPHENE, Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2015 |
| Předmět: |
Class (set theory)
FOS: Physical sciences topological superconductor 02 engineering and technology 01 natural sciences Theoretical physics Dimension (vector space) 0103 physical sciences Bound state Mesoscale and Nanoscale Physics (cond-mat.mes-hall) braiding General Materials Science Invariant (mathematics) 010306 general physics Physics [PHYS]Physics [physics] Condensed Matter - Mesoscale and Nanoscale Physics Pacs Numbers: 73.20.-r 73.63.Nm 74.78.Fk 021001 nanoscience & nanotechnology Condensed Matter Physics MAJORANA Character (mathematics) Symmetry (geometry) 0210 nano-technology Mirror symmetry Majorana |
| Zdroj: | Journal of Physics C: Solid State Physics Journal of Physics C: Solid State Physics, Institute of Physics (IOP), 2015, 27 (45), pp.455601. ⟨10.1088/0953-8984/27/45/455601⟩ Journal of Physics C: Solid State Physics, 2015, 27 (45), pp.455601. ⟨10.1088/0953-8984/27/45/455601⟩ |
| ISSN: | 1361-648X 0022-3719 |
| DOI: | 10.1088/0953-8984/27/45/455601⟩ |
| Popis: | In this paper we demonstrate under what conditions a pseudo-spin degree of freedom or character can be ascribed to the Majorana bound states (MBS) which can be created at the end of one dimensional non-interacting systems, corresponding to D, DIII and BDI in the usual classification scheme. We have found that such a character is directly related to the class of the topological superconductor and its description by a $\mathbb{Z}$, rather than a $\mathbb{Z}_2$, invariant which corresponds to the BDI class. We have also found that the DIII case with mirror symmetry, which supports multiple MBS, is in fact equivalent to the BDI class with an additional time-reversal symmetry. In all cases where a character can be given to the Majorana states we show how to construct the appropriate operator explicitly in various examples. We also examine the consequences of the Majorana character by considering possible hybridization of MBS brought into proximity and find that two MBS with the same character do not hybridize. Finally, we show that having this character or not has no consequence on the braiding properties of MBS. Comment: 10 pages, 1 figure |
| Databáze: | OpenAIRE |
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