Skip to Main content Skip to Navigation
Journal articles

Majoranas with and without a 'character': hybridization, braiding and Majorana number

Abstract : 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.
Document type :
Journal articles
Complete list of metadatas

Cited literature [37 references]  Display  Hide  Download

https://hal-cea.archives-ouvertes.fr/cea-01334652
Contributor : Emmanuelle de Laborderie <>
Submitted on : Tuesday, June 21, 2016 - 10:27:08 AM
Last modification on : Wednesday, October 14, 2020 - 3:41:27 AM
Long-term archiving on: : Thursday, September 22, 2016 - 10:53:28 AM

File

1501.02748v4.pdf
Files produced by the author(s)

Identifiers

Citation

N. Sedlmayr, M. Guigou, P. Simon, C. Bena. Majoranas with and without a 'character': hybridization, braiding and Majorana number. Journal of Physics C: Solid State Physics, Institute of Physics (IOP), 2015, 27 (45), pp.455601. ⟨10.1088/0953-8984/27/45/455601⟩. ⟨cea-01334652⟩

Share

Metrics

Record views

123

Files downloads

151