トポロジカル絶縁体の場の理論と素粒子の統一模型の研究

Material type: 文書・図像類

Author: 藤原,, 高徳ほか

Publisher: 茨城大学理学部

Publication date: 2017-06-23

Material Format: Digital

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Material Type: 文書・図像類
Title: トポロジカル絶縁体の場の理論と素粒子の統一模型の研究
Author/Editor: 藤原,, 高徳
Fujiwara,, Takanori
Author Heading: 藤原,, 高徳
Fujiwara,, Takanori
Publication, Distribution, etc.: 茨城大学理学部
Publication Date: 2017-06-23
Publication Date (W3CDTF): 2017-06-23
Alternative Title: Investigation of the field theories for topological insulators and unified　models of elementary particles
Text Language Code: jpn
Target Audience: 一般
Note (General): application/pdf
text/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.
Access Restrictions: 限定公開
Data Provider (Database): 国立情報学研究所 : 学術機関リポジトリデータベース（IRDB）（機関リポジトリ）
https://irdb.nii.ac.jp
Original Data Provider (Database): 茨城大学 : 茨城大学学術情報リポジトリ