The Hall conductance, topological quantum phase transition and the Diophantine equation on honeycomb lattice
| dc.creator | Sato, Masatoshi | |
| dc.creator | Tobe, Daijiro | |
| dc.creator | Kohmoto, Mahito | |
| dc.date | 2008-08-26 | |
| dc.date | 2008-11-06 | |
| dc.date.accessioned | 2026-07-07T12:59:22Z | |
| dc.date.available | 2026-07-07T12:59:22Z | |
| dc.description | We consider a tight-binding model with the nearest neighbour hopping integrals on the honeycomb lattice in a magnetic field. Assuming one of the three hopping integrals, which we denote t_a, can take a different value from the two others, we study quantum phase structures controlled by the anisotropy of the honeycomb lattice.For weak and strong t_a regions, respectively, the Hall conductances are calculated algebraically by using the Diophantine equation. Except for a few specific gaps, we completely determine the Hall conductances in these two regions including those for subband gaps. In a weak magnetic field, it is found that the weak t_a region shows the unconventional quantization of the Hall conductance, σ_{xy}=-(e^2/h)(2n+1), (n=0,\pm 1,\pm 2,...), near the half-filling, while the strong t_a region shows only the conventional one, σ_{xy}=-(e^2/h)n,(n=0,1,2,...). From topological nature of the Hall conductance, the existence of gap closing points and quantum phase transitions in the intermediate t_a region are concluded. We also study numerically the quantum phase structure in detail, and find that even when t_a=1, namely in graphene case, the system is in the weak t_a phase except when the Fermi energy is located near the van Hove singularity or the lower and upper edges of the spectrum. | |
| dc.description | 35 pages, 15 figures; added references | |
| dc.identifier | https://arxiv.org/abs/0808.3440 | |
| dc.identifier | http://arxiv.org/abs/0808.3440 | |
| dc.identifier | Phys. Rev. B78, 235322 (2008) | |
| dc.identifier | doi:10.1103/PhysRevB.78.235322 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/225549 | |
| dc.subject | Mesoscale and Nanoscale Physics | |
| dc.title | The Hall conductance, topological quantum phase transition and the Diophantine equation on honeycomb lattice | |
| dc.type | text |