Existence of a Sharp Anderson Transition in Disordered Two-Dimensional Systems

  • G. M. Scher
  • D. Adler
Part of the Institute for Amorphous Studies Series book series (IASS)


We derive the quantum-mechanical energy-dependent diffusivity directly from the Kubo-Greenwood formula for electrical conductivity. The resulting expression suggests a numerical method for the solution of the Schrodinger equation without the introduction of sample boundaries. Instead, we simply analyze the diffusion of a particle outwards from an initial bulk site. This method is applied to calculate the conductivity of a two-dimensional system in the presence of various degrees of time-independent disorder. In the case of the Anderson model for non-interacting electrons, we find a sharp transition from localized to diffusive behavior, contrary to the predictions of scaling theory.

Photographs of the energy-resolved electronic probability waveform during its evolution in time indicate a phenomenon similar to classical percolation, but with the distinct quantum feature of a minimum metallic conductivity, as predicted by Mott. An explanation of the numerical results is based on first principles and utilizes only the essential physical ingredients of the problem: disorder diffusion, and quantum-mechanical probability amplitude.


Diffusive Behavior Anderson Model Schrodinger Equation Band Center Anderson Localization 
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Copyright information

© Plenum Press, New York 1985

Authors and Affiliations

  • G. M. Scher
    • 1
  • D. Adler
    • 2
  1. 1.Hewlett-Packard CompanyFort Collins Integrated Circuits DivisionUSA
  2. 2.Center for Materials Science and EngineeringMassachusetts Institute of TechnologyUSA

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