The triangular vortex lattices in the Kitaev honeycomb model

Abstract

This thesis aims to study the vortex lattices in the Kitaev honeycomb model in the presence of time-reversal breaking term. The gapped spectrum in the Kitaev model is characterized by a Chern number and the system hosts anyonic excitations. This project aims at finding these 16 types of phases within the Kitaev model in the presence of triangular vortex lattices and build effective models of Majorana fermions to explain the trends.