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Ibaraki University Academic Repository
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Bibliographic Record
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- Material Type
- その他
- Author/Editor
- 藤原,, 高徳Fujiwara,, Takanori
- Author Heading
- Publication, Distribution, etc.
- Publication Date
- 2017-06-23
- Publication Date (W3CDTF)
- 2017
- Alternative Title
- Investigation of the field theories for topological insulators and unified models of elementary particles
- Target Audience
- 一般
- Note (General)
- 出版タイプ： VoRapplication/pdftext/plain研究報告書研究成果の概要（和文）：トポロジカル絶縁体はパラメータの連続変形に対して安定なギャップを持つ絶縁体で、バルクなトポロジカル絶縁体はCern数と呼ばれる位相不変量で特徴づけられることがしられている。有限なトポロジカル絶縁体では特有のエッジ状態が絶縁体表面に現れてギャップが閉じる。この現象を場の理論的に理解し、素粒子の統一模型への応用の可能性を探るために、周期的なトポロジカル絶縁体の格子模型を考案し、外部電磁場に対するエネルギー固有値のレスポンスを調べた。また、場の理論との比較を行うために、一様に磁化されたトーラス上のDirac演算子のスペクトルの解析を行い、ゼロ・モード解の厳密な構成方法を与えた。研究成果の概要（英文）：Topological insulators have a gap that is stable under continuous deformation of parameters. It is known that a bulk topological insulator is characterized by a topological invariant called such as the Chern number. In finite topological insulators there appear characteristic edge states at the surface and the gap closes. To get insight into the phenomena and seek for possible application to unified theories of elementary particles we have introduced periodic lattice models of topological insulators and investigated the response of energy epectra with applied electromagnetic fields. To compare field theoretical approaches we have also studied the eigenvalue problem for Dirac operators on uniformly magnetized tori in arbitary dimensions and give a construction of exact zero-mode solutions.