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

Abstract

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.

12 pages, final version

References in corpus (6)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Non-Abelian Anyons and Topological Quantum Computation
• Classification of topological insulators and superconductors in three spatial dimensions
• Chiral Topological Superconductor From the Quantum Hall State
• Quantizing Majorana Fermions in a Superconductor
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Cited by in corpus (2)

• Spectral flows associated to flux tubes
• Characterizing the weak topological properties: Berry phase point of view