@article{oai:kumadai.repo.nii.ac.jp:00026687,
 author = {長谷川, 泰正 and 岸木, 敬太 and Hasegawa, Yasumasa and Kishigi, Keita},
 issue = {16},
 journal = {Physical Review B : Condensed Matter and Materials Physics},
 month = {Oct},
 note = {application/pdf, 論文(Article), 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(ε) ∝ |ε|1/3 when three Dirac points merge, and
D(ε) ∝ |ε|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., http://prb.aps.org/abstract/PRB/v86/i16/e165430},
 pages = {165430-1--165430-18},
 title = {Merging Dirac points and topological phase transitions in the tight-binding model on the generalized honeycomb lattice},
 volume = {86},
 year = {2012}
}