The Anderson Transition and the Nonlinear σ-Model

  • F. J. Wegner
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 39)


A particle (e.g. an electron) moving in a random one-particle tight-binding potential
$$H = \sum\limits_{r,{r^1}} {{v_{r,{r^1}}}\left| {r > < {r^1}} \right|}$$
may have localized and extended eigenstates depending on the energy of the particle. The energy Ec which separates the localized states from the extended states is called the mobility edge. Extended states can carry a direct current whereas localized states are bound to a certain region and can move only with the assistance of other mechanisms (e.g. by phonon-assisted hopping). Thus the residual d.c. conductivity is expected to vanish for Fermi energies E in the region of localized states, and to be nonzero for E in the region of the extended states.


Extended State Mobility Edge Symplectic Case Anderson Transition Symmetry Breaking Term 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1982

Authors and Affiliations

  • F. J. Wegner
    • 1
  1. 1.Institut für Theoretische PhysikRuprecht-Karls-UniversitätHeidelbergFed. Rep. of Germany

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