| Project/Area Number |
10640321
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
固体物性Ⅱ(磁性・金属・低温)
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| Research Institution | HOKKAIDO UNIVERSITY |
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Principal Investigator |
YAKUBO Kousuke Hokkaido Univ., Grad. School of Eng., Asso. Prof., 大学院・工学研究科, 助教授 (40200480)
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| Co-Investigator(Kenkyū-buntansha) |
NAKATYAMA Tsuneyoshi,Kousuke Hokkaido Univ., Grad. School of Eng., Prof., 大学院・工学研究科, 教授 (80002236)
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| Project Period (FY) |
1998 – 1999
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| Project Status |
Completed (Fiscal Year 1999)
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| Budget Amount *help |
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 1999: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 1998: ¥2,200,000 (Direct Cost: ¥2,200,000)
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| Keywords | Random Magnetic Field / Localization / Finite-Size Scaling / Multifractal / Universality Class / Fractional Quantum Hall Effect / 強制振動子法 / スーパー・コンピュータ / 大規模行列 / 応答関数 / 久保公式 |
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| Research Abstract |
In recent years there has been a growing interest in two-dimensional electrons in a random magnetic field. Instead of importance of the problem, there still exist many unsolved questions in this field. We have studies the localization property of two-dimensional electrons in random magnetic fields in terms of a novel finite-size scaling based on the multifractality of the critical wave function. At first, we have determined the existence of the metal-insulator transition in a system subject to a random magnetic field with vanishing mean and its universality class. The result suggests that all electronic states are localized in such systems. We also investigated systems in a random magnetic field with finite mean. In the case that the average field is much stronger than the magnitude of field fluctuations, the spectrum separates into Landau subbands and only the states at subband centers are extended as predicted by a semiclassical theory. We confirmed that the universality class of this transition is the same with that of the integer quantum Hall system. Furthermore, the energy of the extended state shifts upward from the subband center when the magnitude of field fluctuation becomes stronger. These results are quite important for understanding electron transport in a fractional quantum Hall system near v=1/2.
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