2007 Fiscal Year Final Research Report Summary
Method of computing Hall conductivities on discrete Brillouin zone-topological quantum numbers on lattices-
| Project/Area Number |
18540365
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | Ibaraki University |
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Principal Investigator |
FUKUI Takahiro Ibaraki University, College of sciences, professor (10322009)
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| Project Period (FY) |
2006 – 2007
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| Keywords | Quantum spin Hall effect / lattice computation / Z2 topological invariant / graphene / bismuth / antimony |
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| Research Abstract |
The purposes of this research are 1) to develop an efficient method of computing topological invariants and 2) its application to realistic materials. In 2006, we had a big progress in computing the first Chern numbers for quantum Hall effect. In 2007, we succeeded in computing the Z2 topological invariant which characterizes the quantum spin Hall effect. What we have achieved are summarized as follows:
1) Quantum Hall effect in graphene: We have computed the Hall conductance of graphene over the whole energy region. We have shown that in between the van-Hove singuralities, Dirac -like quasi-particles exist.
2) Basic algorism of computing Z2 invariant for quantum spin Hall effect: We have developed an efficient algorism and applied it to a simple but typical model, I.e., graphene with spin-orbit couplings. We have shown that out method is indeed simple enough to classify the two phases of graphene.
3) Application of the above algorism to three dimensional materials: We have computed the Z2 invariants for the bulk Bi and Sb as well as their thin films. Since these materials are semi-metal, we do not expect the quantum spin Hall effect. But we have suggested that their thin films become insulators and could show the quantum spin Hall effect.
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