Mean field theory and ϵ-expansion for Anderson localization
We present a field theoretic formulation of Anderson localization of an electron in a random potential. In mean field theory we find a mobility edge at energy E c separating a region with no states from one with conducting states. When the nearest neighbor hopping is a random variable with variance...
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| Published in | Solid state communications Vol. 34; no. 5; pp. 343 - 346 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.01.1980
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| Online Access | Get full text |
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| Summary: | We present a field theoretic formulation of Anderson localization of an electron in a random potential. In mean field theory we find a mobility edge at energy
E
c
separating a region with no states from one with conducting states. When the nearest neighbor hopping is a random variable with variance σ,
E
c
2=4
zσ
2, where
z is the coordination number. We study this mobility edge using the ϵ-expansion. We find an upper critical dimension of eight near which this mobility transition is in the same universality class as the statistics of dilute branched polymers (lattice animals). |
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| ISSN: | 0038-1098 1879-2766 |
| DOI: | 10.1016/0038-1098(80)90571-2 |