Majorana flat band edge modes of topological gapless phase in 2D Kitaev square lattice.
Sci Rep 2019;
9:4978. [PMID:
30899042 PMCID:
PMC6428827 DOI:
10.1038/s41598-019-41529-y]
[Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2018] [Accepted: 03/06/2019] [Indexed: 11/09/2022] Open
Abstract
We study a Kitaev model on a square lattice, which describes topologically trivial superconductor when gap opens, while supports topological gapless phase when gap closes. The degeneracy points are characterized by two vortices in momentum space, with opposite winding numbers. We show rigorously that the topological gapless phase always hosts a partial Majorana flat band edge modes in a ribbon geometry, although such a single band model has zero Chern number as a topologically trivial superconductor. The flat band disappears when the gapless phase becomes topologically trivial, associating with the mergence of two vortices. Numerical simulation indicates that the flat band is robust against the disorder.
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