| 研究課題/領域番号 |
16F16728
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| 研究種目 |
特別研究員奨励費
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| 配分区分 | 補助金 |
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| 応募区分 | 外国 |
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| 研究分野 |
幾何学
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| 研究機関 | 東北大学 |
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研究代表者 |
小谷 元子 東北大学, 理学研究科, 教授 (50230024)
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| 研究分担者 |
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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| 研究期間 (年度) |
2016-11-07 – 2019-03-31
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| 研究課題ステータス |
完了 (2017年度)
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| 配分額 *注記 |
2,000千円 (直接経費: 2,000千円)
2017年度: 1,000千円 (直接経費: 1,000千円)
2016年度: 200千円 (直接経費: 200千円)
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| キーワード | Topological phases / operator algebras / Kasparov theory / aperiodic media |
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| 研究実績の概要 |
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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| 現在までの達成度 (段落) |
翌年度、交付申請を辞退するため、記入しない。
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| 今後の研究の推進方策 |
翌年度、交付申請を辞退するため、記入しない。
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