| Project/Area Number |
16F16728
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| Research Category |
Grant-in-Aid for JSPS Fellows
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| Allocation Type | Single-year Grants |
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| Section | 外国 |
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| Research Field |
Geometry
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| Research Institution | Tohoku University |
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Principal Investigator |
小谷 元子 東北大学, 理学研究科, 教授 (50230024)
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| Co-Investigator(Kenkyū-buntansha) |
BOURNE CHRISTOPHER 東北大学, 理学(系)研究科(研究院), 外国人特別研究員
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| Project Period (FY) |
2016-11-07 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 2017: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2016: ¥200,000 (Direct Cost: ¥200,000)
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| Keywords | Topological phases / operator algebras / Kasparov theory / aperiodic media |
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| Outline of Annual Research Achievements |
We have previously identified Delone sets as a useful model for atomic configurations at low temperature and without any assumptions on the periodicity or structure of the material. We have now developed a framework to understand the topological phases of systems in material science and meta-materials that can be modelled by a Delone configuration. In recent work, we were able to prove the quantization of the so-called bulk complex topological phases of Delone materials. This result gives a prediction of conductivity properties of Delone and aperiodic lattices that appears to be new and novel. In particular, we provide a mathematical theorem and strong numerical evidence that a quantum Hall like effect is possible in aperiodic and amorphous metals, e.g. metallic glass. Interesting future research would be to investigate whether such properties can be experimentally realized. This paper was submitted in December 2017 and is currently under peer review.
We are also finalizing work that more comprehensively characterizes the topological properties of Delone lattices and topological phases using K-theory. This includes topological phases with anti-linear symmetries such as time reversal symmetry. We also prove the bulk-boundary correspondence and study edge properties of Delone topological materials. We expect to complete this work within the coming weeks.
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| Research Progress Status |
翌年度、交付申請を辞退するため、記入しない。
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| Strategy for Future Research Activity |
翌年度、交付申請を辞退するため、記入しない。
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