Merging of Dirac points in a two-dimensional crystal

Understand

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 semi-metallic 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 alpha-(BEDT-TTF)_2 I_3 or in an optical lattice of cold atoms simulating deformed graphene.