Time-reversal symmetric Kitaev model and topological superconductor in two dimensions

R. Nakai; S. Ryu; A. Furusaki

doi:10.1103/PhysRevB.85.155119

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Time-reversal symmetric Kitaev model and topological superconductor in two dimensions

R. Nakai, S. Ryu, A. Furusaki

DOI 10.1103/PhysRevB.85.155119 · Physical Review B

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Abstract

A time-reversal invariant Kitaev-type model is introduced in which spins (Dirac matrices) on the square lattice interact via anisotropic nearest-neighbor and next-nearest-neighbor exchange interactions. The model is exactly solved by mapping it onto a tight-binding model of free Majorana fermions coupled with static Z2 gauge fields. The Majorana fermion model can be viewed as a model of time-reversal-invariant superconductor and is classified as a member of symmetry class DIII in the Altland-Zirnbauer classification. The ground-state phase diagram has two topologically distinct gapped phases which are distinguished by a Z2 topological invariant. The topologically nontrivial phase supports both a Kramers’ pair of gapless Majorana edge modes at the boundary and a Kramers’ pair of zero-energy Majorana states bound to a 0-flux vortex in the π-flux background. Power-law decaying correlation functions of spins along the edge are obtained by taking the gapless Majorana edge modes into account. The model is also defined on the one-dimension ladder, in which case again the ground-state phase diagram has Z2 trivial and nontrivial phases.