2006 Fiscal Year Final Research Report Summary
Anderson transitions in disordered systems and electron correlations
| Project/Area Number |
16540294
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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 |
Condensed matter physics I
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| Research Institution | Toho University |
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Principal Investigator |
KAWARABAYASHI Tohru Faculty of Science, Associate Professor, 理学部, 助教授 (90251488)
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| Project Period (FY) |
2004 – 2006
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| Keywords | Anderson localization / quantum Hall system / magneto transport / edge states / correlated random potential / random magnetic fields |
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| Research Abstract |
In 2004 and 2005, we have studied the transport properties of the two-dimensional system in a disordered magnetic field with a fixed sign. This model corresponds to the case where the random fluctuation of the magnetic field is of the same order of its mean value. The two-dimensional random magnetic field system arises in the theory of the fractional quantum Hall system where the electron correlation plays an important role. It has then been found for systems without edge states that the conductance is insensitive to the strength of the fluctuation of the magnetic field and stays on the order of the conductance quantum in the limit of weak magnetic fields. This singular behavior can be understood within the framework of the Drude formula. Apart from this classical singularity in the weak field limit, we have also shown that the Shubnikov-de Haas effect is clearly seen in this system.
We have also investigated the statistical properties of the conductance in such a system. In particular,
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the critical conductance distribution has been analyzed in detail. In the presence of edge states, it has been shown that the critical distribution of conductance exhibits a wide distribution whose width is of the order of the conductance quantum. For systems with no edge state, the critical distribution similar to that for the network model and that for the model with potential disorder has been obtained, suggesting the universality of the critical distribution.
In 2006, we have studied the effect of potential correlation in quantum Hall wires and found unexpected feature introduced by the potential correlation. In real materials, the impurity potential has a finite potential range and thus the disorder potential has a finite correlation length. It is therefore important to consider the effect of potential correlation as well as the electron correlation. In the absence of impurities, the conductance of the quantum Hall wire exhibits the quantized steps at the bulk Landau levels. In the presence of impurities, the impurity scattering mixes the edge states with the bulk states and the conductance becomes exponentially small at the conductance plateau transitions. We have found that when the potential correlation length is larger than the magnetic length, the small conductance region disappears as expected. Apart from it, we have also found unexpectedly that the conductance steps shift toward higher energies. This new feature is specific to long wires. We have argued semi-classically that the shift is a consequence of the reflection of edge states due to smoothly varying disorder potential. Less
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Research Products
(6 results)
