2017 Fiscal Year Research-status Report
クーロン相互作用する電子系におけるアンダーソン転移への新規なアプローチ
| Project/Area Number |
26400393
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| Research Institution | Osaka University |
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Principal Investigator |
SLEVIN KEITH 大阪大学, 理学研究科, 准教授 (90294149)
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| Project Period (FY) |
2014-04-01 – 2019-03-31
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| Keywords | doped semiconductors / Coulomb interaction / quantum Hall effect / Anderson transition |
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| Outline of Annual Research Achievements |
In semiconductors there is a transition from an insulating to a metallic state as the doping concentration is increased. This is thought to be a type of Anderson transition. We are using computer simulations to understand this transition better.
The beta-function plays a central role in the theory of the Anderson transition. We published Borel-Pade re-summations of the beta-functions in the three Wigner-Dyson symmetry classes. (with Y. Ueoka)
We adapted the transfer matrix method used extensively in Anderson localisation so that it can run efficiently on massively parallel supercomputers. (with T. Ohtsuki.)
We continued to investigate ways of using machine learning to analyse wave functions produced in the simulation of the doped semiconductor. (with Y. Harashima, T. Mano, T. Ohtsuki)
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
While difficulties have been encountered in the analysis of the wave functions produced in the simulations, we continue to investigate new ways of analysing these using machine learning techniques.
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| Strategy for Future Research Activity |
We will continue to investigate different ways of analysing the wavefunction data from the simulation of the doped semiconductor.
Recently, based on studies in lattice models, it has been suggested that the critical exponent for the quantum Hall effect in the Chalker-Coddington model may be anomalous and not universal. This calls into question the attribution of the disagreement between the experimentally measured exponent and the value for the Chalker-Coddington model to the effect of the Coulomb interaction. We feel that the precision of current reported studies is however not sufficient to reach a definitive conclusion and we are actively considering more precise studies.
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| Causes of Carryover |
[Reason]
Upgrade of some computer hardware was postponed until this year pending availability of improved hardware.
[Usage Plan]
Upgrade of computer hardware. Upgrade and renewal of necessary software licenses. Travel expenses for participation in relevant workshops and conferences.
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