Merging Dirac points and topological phase transitions in the tight-binding model on the generalized honeycomb lattice

Abstract

Moving, merging, and annihilating Dirac points are studied theoretically in the tight-binding model on honeycomb lattice with up-to third-nearest-neighbor hoppings. We obtain a rich phase diagram of the topological phase transitions in the parameter space of direction-dependent hoppings. We obtain the conditions for the three Dirac points to merge and for the tricritical points. We find that only very small third-nearest-neighbor hoppings are enough for the existence of the merging of three-Dirac-points and the tricritical points, if the system is sufficiently anisotropic. The density of states is obtained to be $D(\ensuremath{\epsilon})\ensuremath{\propto}{|\ensuremath{\epsilon}|}^{1/3}$ when three Dirac points merge, and $D(\ensuremath{\epsilon})\ensuremath{\propto}{|\ensuremath{\epsilon}|}^{1/4}$ at the tricritical points. It is possible to realize these topological phase transitions in the ultracold atoms on the optical lattice, strained monolayer graphene, or strained bilayer graphene.