Localized zero-energy modes in the Kitaev model with vacancy disorder

Santhosh G., V. Sreenath, Arul Lakshminarayan, and Rajesh Narayanan

Phys. Rev. B 85, 054204 – Published 21 February 2012

Abstract

We study the effects of vacancy disorder on the Kitaev model defined on a hexagonal lattice. We show that the vacancy disorder induces a zero mode that is localized at the defect site. We derive analytical forms for these localized wave functions in both the gapped and gapless phases of the Kitaev model. We conjecture that the vacancy disorder can be utilized as a probe of the quantum phase transition (from the gapped to gapless phases) in this model. The behavior of the inverse participation ratio in the gapless phase and across the transition is also studied numerically. Comments are made about the behavior of site-site entanglement in the single-particle states for the case of a single vacancy.