{ "id": "1207.6841", "version": "v1", "published": "2012-07-30T05:48:28.000Z", "updated": "2012-07-30T05:48:28.000Z", "title": "Merging Dirac points and topological phase transitions in the tight-binding model on the generalized honeycomb lattice", "authors": [ "Yasumasa Hasegawa", "Keita Kishigi" ], "comment": "19 pages, 25 figures", "journal": "Phys. Rev. B 86, 165430 (2012)", "doi": "10.1103/PhysRevB.86.165430", "categories": [ "cond-mat.mes-hall", "cond-mat.str-el" ], "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.", "revisions": [ { "version": "v1", "updated": "2012-07-30T05:48:28.000Z" } ], "analyses": { "subjects": [ "73.22.Pr", "73.43.Nq", "71.10.Pm", "73.20.At" ], "keywords": [ "topological phase transitions", "generalized honeycomb lattice", "merging dirac points", "tight-binding model", "tricritical points" ], "tags": [ "journal article" ], "publication": { "publisher": "APS", "journal": "Physical Review B", "year": 2012, "month": "Oct", "volume": 86, "number": 16, "pages": 165430 }, "note": { "typesetting": "TeX", "pages": 19, "language": "en", "license": "arXiv", "status": "editable", "adsabs": "2012PhRvB..86p5430H" } } }