Savoyan Castle, Rackeve, Hungary. Workshop on Disorder and Interactions . Disordered Electron Systems I. Introduction Scaling theory Microscopic theory Non-interacting case. Roberto Raimondi. Thanks to C. Di Castro C. Castellani. 4-6 april 2006.
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Key physics:quantum interference corrections
G. Bergman Phys. Rep. 107, 1 (1984)
P.A. Lee and T.V. Ramakrishnan Rev. Mod. Phys. 57, 287 (1985)
B.L. Altshuler and A.G. Aronov in Electron-electron Interactions in Disordered Systems,
Eds. M.Pollak and A.L. Efros North-Holland, Amsterdam (1984) p.1
A.M. Finkelstein Sov. Sci. Rev.14, 1 (1990)
D. Belitz and T.R. Kirkpatrick Rev. Mod. Phys. Rep. 66, 261 (1994)
C. Di Castro and R. Raimondi in The Electron Liquid Paradigm in Condensed Matter Physics
Proceedings of the Inter. School of Physics E. Fermi,
Eds. G.F. Giuliani and G. Vignale IOP Press 20041. Cond-mat/0402203
Random walk of step
Response function and Einstein’s relation
Fermi gas case:
Summing all times
Task for microscopic theory:
Diffusion modes as critical modes
Inverse conductivity as expansion parameter
Edwards and Thouless 1972
Control parameter: dimensionless conductance
Depends on g only
Abrahams, Anderson, Licciardello, Ramakrishnana 1979
Metallic side expansion
Time reversal invariance
B-field or magnetic impurities
Castellani, Di Castro, Forgacs, Tabet 1983
Consequences of W.i.
Phenomenological theory obeys all !
Task: recover semiclassical approach as the zeroth order in
Disorder expected effect
Disorder model: Gaussian random variable
Self-consistent solution, only position of the pole matters
Abrikosov, Gorkov, Dzyaloshinski
Langer, Neal 1976
Recover the semiclassical result!
Role of crossed diagrams
Maximally crossed diagrams
Enhanced backscattering due to time-reversed paths
Weak localization correction
Gorkov, Larkin, Khmelnitskii 1979
Crossed diagrams in real space
B enters via
a “mass” in the diffusion propagator
Singlet and Triplet channels
WL seen in films and wires
Compensated Smc and alloys
Si-P critical exponent puzzle
Si As n-doped, Si B p-doped
CuMn Magnetic impurities ?
Okuma et al ‘87
Katsumoto et al JPSJ ‘87
Si Au Strong Spin Orbit
Nishida et al SSP ‘84
Singularity in DOS
Key issue: how e-e interaction changes the game?
Kravchenko and SarachikRep. Progr. Phys.67, 1 (2004)