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

TL;DR

This paper theoretically investigates the merging and annihilation of Dirac points in a honeycomb lattice model with extended hoppings, revealing rich topological phase transitions and specific density of states behaviors.

Contribution

It provides the conditions for Dirac point merging and tricritical points in a generalized honeycomb lattice with up to third-nearest-neighbor hoppings, highlighting the effects of anisotropy.

Findings

Small third-nearest-neighbor hoppings induce Dirac point merging.

Density of states scales as |psilon|^{1/3} at merging points.

Topological phase transitions can be realized in ultracold atoms and strained graphene.

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 $D(\epsilon) \propto |\epsilon|^{1/3}$ when three Dirac points merge, and $D(\epsilon) \propto |\epsilon|^{1/4}$ 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.