Disordered Electron Systems Roma Tre University无序电子系统罗马第三大学.ppt

Disordered Electron Systems I. Roberto Raimondi Classically transport is described as a random walk. This implies the diffusive form of the response function and Einstein’s relation connecting the phenomenological coefficients as diffusion constant, conductivity, and compressibility. * Introduction Scaling theory Microscopic theory Non-interacting case Thanks to C. Di Castro C. Castellani Workshop on Disorder and Interactions Savoyan Castle, Rackeve, Hungary 4-6 april 2006 MIT from interplay of disorder and interaction Metallic side in terms of Fermi liquid Aim: describe MIT as continuous phase transition Tasks:identify couplings and critical modes Key problem: metal-insulator transition (MIT) 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 Semiclassical theory: Drude-Boltzmann-Sommerfeld Random walk of step Diffusive motion Response function and Einstein’s relation Fermi gas case: Quantum corrections: self-intersecting trajectories Return probability Self-intersection probability Summing all times Task for microscopic theory: Diffusion modes as critical modes Inverse conductivity as expansion parameter Scaling theory Thouless’s argument Control parameter: dimensionless conductance Edwards and Thouless 1972 Scaling hypothesis: Depends on g only Fixed point: Critical exponent: Abrahams, Anderson, Licciardello, Ramakrishnana 1979 Power behavior of physical quantities Correlation length Scal