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Electrons in disordered systems

V.S. Khrapai

Lecture 1.Metal-insulator transitions. Disorder-driven transitions: Anderson model and model of structural disorder. Mott transition. Minimal metallic conductance.

Lecture 2.Physical aspects of the percolation theory. Effective medium approximation. Problems of sites and bonds. Percolation in a system of random sites. Continual problems. Percolation thresholds and critical indexes .

Lecture 3.Electronic structure of the impurity band in semiconductors with low doping level. Coulomb gap. Measurements of the electronic spectrum by tunneling spectroscopy.

Lecture 4.Transitions between the localized states. Various types of hopping conduction: nearest-neighbor and variable-range hopping. Mott and Efros-Shklovskii laws.

Lecture 5.Hopping conduction in finite size samples. Does Mott law exist in 1D?

Lecture 6.Weak localization and quantum corrections to the conductivity. Optical analogy of the weak localization. Antilocalization. Rate of electron-electron collisions in the dirty limit. Aronov-Altshuler effect.

Lecture 7.Scaling hypothesis. Conductance in a critical region of the metal-insulator transition in 3D. Quantum phase transition. 1D and 2D systems. Scaling and spin-orbital interaction.

Lecture 8.Landauer formalism in 1D systems. Localization and role of correlated disorder.

Lecture 9.Interactions in 1D systems. Luttinger liquid. Bosonic excitations. Tunneling into the Luttinger liquid.

Lecture 10.Granular metals. Coulomb blockade and its role in metal-insulator transitions.

Lecture 11. Disordered systems with high electron density. Liquid metals. Zaiman theory. Chemical localization.

Lecture 12. Integer Quantum Hall effect. Spectrum of 2D electrons in perpendicular magnetic field. Mechanism of the plateau formation. Fractional quantum Hall effect.

  1. V.F. Gantmakher Electrons in disordered systems, Fizmatlit, 2005.
  2. B.I.Shklovskii and A.L. Efros Electronic properties of doped semiconductors. Nauka, 1979
  3. N.Mott E.Davies Electronic processes in noncrystalline systems, 1982.
  4. T. Giamarchi Quantum Physics in One Dimension, Oxford, 2003.
  5. J. Imry Introduction to mesoscopic physics, Fizmatlit, 2004.
  6. A. Efros Physics and geometry of the disorder, A tiny library of Quantum, iss.19, 1982.

Agarkov D.A. Tel: +7(916)7584930 email: agarkov@issp.ac.ru