Merging of Dirac points in a two-dimensional crystal

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 α-(BEDT-TTF)₂I₃ or in an optical lattice of cold atoms simulating deformed graphene.