Studies on spectral band structures on carbon nanotubes and their related topics

2021 Fiscal Year Final Research Report

• Project/Area Number: 17K14221
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Mathematical analysis
• Research Institution: Maebashi Institute of Technology
• Principal Investigator: Niikuni Hiroaki 前橋工科大学, 工学部, 准教授 (90609562)
• Project Period (FY): 2017-04-01 – 2022-03-31
• Keywords: シュレディンガー方程式・作用素 / スペクトル理論 / 周期ポテンシャル / 量子グラフ / カーボンナノチューブ / グラフェン / 埋蔵固有値 / Shnol 型定理

Outline of Final Research Achievements

Throughout this project, we studied spectral structure of Schroedinger operators on various types of carbon nanotubes from the point of view of the corresponding quantum graph (the differential operators on the metric graphs). The first model is a periodically broken carbon nanotube. The second one is a zigzag supergraphene-based carbon nanotube. The third one is zigzag carbon nanotube with multiple bonds. The last one is a zigzag carbon nanotube with impurities.

In the field of the solid states physics, topological insulators are outstanding materials, which behave as an insulatorin their interior but contain conducting states on their surfaces. In order to consider this nature by the method of quantum graph, we compared the spectra of Schrodinger operators on graphene as the whole space with graphene with zigzag boundaries.

Free Research Field

数学

Academic Significance and Societal Importance of the Research Achievements

カーボンナノチューブ・グラフェンは, 現代の科学技術において欠くことのできない材料であり, その性質を解明することは現代産業を支える社会的意義を有する。特に, それらの電気伝導性の性質は, 対応するシュレディンガー方程式のスペクトルの性質を調べることで数学的に解明される。