Majorana fermions and Z$_2$ vortices on a square lattice

Details Majorana fermions and Z$_2$ vortices on a square lattice Majorana fermions and Z$_2$ vortices on a square lattice

2011-09-09

arxiv.org/abs/1109.1926v2

J. Phys. Soc. Jpn. 80 (2011) 123708

Physics

Condensed Matter

Superconductivity

12 pages, final version

Scientific paper

10.1143/JPSJ.80.123708

We present a simple model of Majorana fermions on a square lattice, and study zero-energy states due to Z$_2$ vortices. We show the relationship between the Chern number of the ground state and the number of the zero-energy states by numerical calculations for finite systems. We also discuss the relationship for the bulk system by observing the change of the spectral asymmetry. We finally present an effective continuum model with O(2) gauge potential which shows a topological change of the index at a half-flux.

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