A new approach to the Anderson transition in electron systems with Coulomb interactions

2018 Fiscal Year Final Research Report

• Project/Area Number: 26400393
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Osaka University
• Principal Investigator: Slevin Keith 大阪大学, 理学研究科, 准教授 (90294149)
• Research Collaborator: Ohtsuki Tomi ; Kettemann Stefan ; Harashima Yosuke
• Project Period (FY): 2014-04-01 – 2019-03-31
• Keywords: disordered systems / Anderson transition / critical phenomena

Outline of Final Research Achievements

Using extensive numerical simulations, this project has contributed to a better understanding of the critical phenomena of the Anderson transition both in simplified models, and in more realistic models of the metal-insulator transition in doped semiconductors. We studied the dimensionality dependence of the critical exponent of the Anderson transition in simplified models in detail numerically and found the results to be in reasonable agreement with analytical predictions. We also studied the effect of magnetic impurities on the Anderson transition and found the results to be consistent with analytical theoretical predictions. We also found evidence that the critical exponent (and hence the universality class of the phase transition) is changed by the long-range Coulomb interaction between electrons.

Free Research Field

物性理論

Academic Significance and Societal Importance of the Research Achievements

本プロジェクトは，ランダムポテンシャルと電子 - 電子相互作用の両方を含む問題を扱っている。この問題は，物性物理学において最も困難なものの一つである。この研究プロジェクトの学術的意義は2つあると思われる。まず、この研究はアンダーソン遷移を説明するために提案された理論的な考え方が正しいという確信を与えた。第二に、この研究はランダムポテンシャルと電子 - 電子相互作用を（近似的にではあるが）同等に扱う研究への道を示唆した。