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Anderson Localization in Random Potential with Long Range Correlation

Lotfallahzadeh, Shiva | 2014

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 45330 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Rahimi Tabar, Mohammad Reza
  7. Abstract:
  8. In a one-dimensional disordered system, Anderson localization is known to occur at any energy in the thermodynamic limit when the disorder is uncorrelated and white noise structure.
    A great interest for 1D disordered models with correlated disorder has been growing since 2002, as it has become progressively clear that the correlation of the random potentials can deeply affect the electronic localization properties. Spatial correlation of disorder can unexpectedly create extended states at some particular energies.
    In this thesis, we study the metal-insulator transition in one dimensional Anderson binary alloy with long range disordered hopping integral and on-site energy, using the transfer-matrix method. In this model the on-site energies and hopping integrals are distributed randomly with long range correlations characterized by power spectrum of the type; S(k)=k^(-(2α-1)), with different exponents α_εand α_t, respectively. We determine the critical value of long range correlation exponent of hopping integral α_(t,c) in the presence of solely off-diagonal disorder in which the transition form localized to extended states occurs in thermodynamic limit. When both of the on-site energies and hopping integrals are disordered, there are two parameters α_t and α_εthat control the metal - insulator transition in the system. We find the phase diagram which separates the localized regime from extended one and it shows the critical values of α_t for given value of α_ε
  9. Keywords:
  10. Anderson Localization ; Metal-Insulator Transition (MIT) ; Electrical Conductivity ; Random Potetial with Long Range Correlation

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