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Universal distribution functions in two-dimensional localized systems.

A M Somoza1, M Ortuño, J Prior

  • 1Departamento de Física-CIOyN, Universidad de Murcia, Murcia 30.071, Spain.

Physical Review Letters
|October 13, 2007
PubMed
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We discovered universal conductance distributions in the 2D Anderson model

Area of Science:

  • Condensed Matter Physics
  • Disordered Systems
  • Quantum Transport

Background:

  • The Anderson model describes electron localization in disordered materials.
  • Understanding conductance distribution is key to characterizing transport properties.

Purpose of the Study:

  • To determine the conductance distribution function in the 2D Anderson model's strongly localized regime.
  • To investigate the dependence of these distributions on lead characteristics.

Main Methods:

  • Analysis of the two-dimensional Anderson model in the strongly localized limit.
  • Investigating the behavior of conductance fluctuations (lng) with varying lateral size (L).

Main Results:

  • Conductance fluctuations grow as L^(1/3) with system size.

Related Experiment Videos

  • A universal Tracy-Widom distribution governs conductance for narrow leads.
  • A related but distinct distribution is observed for wide leads.

    • Conclusions:

    • The conductance distribution in the strongly localized 2D Anderson model exhibits universal behavior.
    • The Tracy-Widom distribution emerges for narrow leads, linking to random matrix theory.
    • Lead width significantly influences the conductance distribution.