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

Moving, merging, and annihilating Dirac points are studied theoretically in the tight-binding model onhoneycomb lattice with up-to third-nearest-neighbor hoppings.We obtain a rich phase diagram of the topologicalphase transitions in the parameter space of direction-dependent hoppings. We obtain the conditions for the threeDirac points to merge and for the tricritical points. We find that only very small third-nearest-neighbor hoppingsare enough for the existence of the merging of three-Dirac-points and the tricritical points, if the system issufficiently anisotropic. The density of states is obtained to be D(ε) ∝ |ε|1/3 when three Dirac points merge, andD(ε) ∝ |ε|1/4 at the tricritical points. It is possible to realize these topological phase transitions in the ultracoldatoms on the optical lattice, strained monolayer graphene, or strained bilayer graphene