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

TL;DR

This paper introduces a time-reversal invariant Kitaev model on a square lattice, exactly solvable via Majorana fermions, revealing topologically distinct phases with edge modes and zero-energy states, advancing understanding of topological superconductors.

Contribution

It presents a novel exactly solvable 2D Kitaev-type model with time-reversal symmetry, classifying its topological phases and analyzing edge states and vortex-bound Majorana modes.

Findings

Identifies two topologically distinct gapped phases with Z_2 invariant.

Demonstrates presence of Kramers' pairs of Majorana edge modes.

Shows zero-energy Majorana states bound to vortices.

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 Z_2 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 Z_2 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 \pi-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 Z_2 trivial and non-trivial phases.