Merging of Dirac points in a two-dimensional crystal

Abstract

We study under which general conditions a pair of Dirac points in the electronic spectrum of a two-dimensional crystal may merge into a single one. The merging signals a topological transition between a semimetallic phase and a band insulator. We derive a universal Hamiltonian that describes the physical properties of the transition, which is controlled by a single parameter, and analyze the Landau-level spectrum in its vicinity. This merging may be observed in the organic salt $\ensuremath{\alpha}\ensuremath{-}{(\text{BEDT-TTF})}_{2}{\text{I}}_{3}$ or in an optical lattice of cold atoms simulating deformed graphene.