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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)

Abstract

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.

Keywords

Diffusive Behavior Anderson Model Schrodinger Equation Band Center Anderson Localization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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