Merging of Dirac points in a two-dimensional crystal

TL;DR

This paper investigates the conditions under which two Dirac points in a 2D crystal merge, causing a topological transition from a semi-metal to an insulator, with a universal Hamiltonian describing the transition.

Contribution

It derives a universal Hamiltonian for Dirac point merging in 2D crystals, applicable to various physical systems, and analyzes the associated topological transition.

Findings

Universal Hamiltonian describes Dirac point merging

Topological transition between semi-metal and insulator

Potential observation in organic salts and cold atom lattices

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 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.