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.
Highlights
The degeneracy points are characterized by two vortices, or Dirac nodal points in momentum space, with opposite winding numbers
We have demonstrated that a topologically trivial superconductor emerges as a topological gapless state, which support Majorana flat band edge modes
There are three parts: (i) We present the Kitaev Hamiltonian on a square lattice and the phase diagram for the topological gapless phase. (ii) We investigate the Majorana bound states. (iii) We perform numerical simulation to investigate the robust of the edge modes against the disorder perturbations
Summary
Topological materials have become the focus of intense research in the last years[1,2,3,4], since they exhibit new physical phenomena with potential technological applications, and provide a fertile ground for the discovery of fermionic particles and phenomena predicted in high-energy physics, including Majorana[5,6,7,8,9,10], Dirac[11,12,13,14,15,16,17] and Weyl fermions[18,19,20,21,22,23,24,25,26]. The Majorana edge modes have been actively pursued in condensed matter physics[27,28,29,30,31,32,33] since spatially separated Majorana fermions lead to degenerate ground states, which encode qubits immune to local decoherence[34] This bulk-edge correspondence indicates that a single-band model must have vanishing Chern number and there should be no edge modes when open boundary conditions are applied. A typical system is a 2D honeycomb lattice of been graphene, which is a zero-band-gap semiconductor with a linear dispersion near the Dirac point There is another interesting feature lies in the appearance of partial flat band edge modes in a ribbon geometry[35,36,37], which exhibit robustness against disorder[38]. Numerical simulation indicates that the flat band is robust against the disorder
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