Coupled Majorana modes in a dual vortex of the Kitaev honeycomb model

Abstract

The Kitaev model is exactly solvable in terms of Majorana fermions hopping on a honeycomb lattice and coupled to a static ${\mathbb{Z}}_2$ gauge field, giving the possibility of $\pi$-vortices in hexagonal plaquettes. In the vortex-full sector and in the presence of a time-reversal-breaking three-spin term of strength $\kappa$, the energy spectrum is gapped and the ground state possesses an even Chern number. An isolated vortex-free plaquette acts as a ``dual vortex'' and binds a fermionic mode at finite energy $\epsilon$ in the bulk gap. This mode is equivalent to two coupled Majorana zero modes located on the same dual vortex. In a continuum approximation, we analytically compute the Majorana wavefunctions and their coupling $\epsilon$ in the two limits of small or large $\kappa$. The analytical approach is confirmed by numerical perturbation theory directly on the lattice. The latter is in excellent agreement with the full numerics on a finite-size system. We contrast our results with states bound to an isolated vortex in a topological superconductor with even Chern number.

17 pages, 9 figures