Fate of Dirac Points in a Vortex Superlattice

TL;DR

This paper investigates how a vortex superlattice affects Dirac points in honeycomb lattice fermions, revealing flux-dependent gap openings and a magnetic field-induced metal-insulator transition relevant to graphene and Kitaev models.

Contribution

It provides an analytical expression for the energy gap induced by vortex superlattices and demonstrates the transition's dependence on superlattice periodicity and flux.

Findings

Gap opens at zero energy depending on superlattice periodicity

Analytical expression for the gap in the small-flux limit

Magnetic field induces a metal-insulator transition in graphene

Abstract

We consider noninteracting fermions on the honeycomb lattice in the presence of a magnetic vortex superlattice. It is shown that depending on the superlattice periodicity, a gap may open at zero energy. We derive an expression of the gap in the small-flux limit but the main qualitative features are found to be valid for arbitrary fluxes. This study provides an original example of a metal-insulator transition induced by a strongly modulated magnetic field in graphene. At the same time our results directly apply to Kitaev's honeycomb model in a vortex superlattice.