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Quantum Phenomena in Nanosystems

Quantum Phenomena in Nanosystems

I.S. Burmistrov (MIPT, Landau Institute for Theoretical Physics)

During last 35 years the great progress was achieved in understanding of quantum phenomena in mesoscopic systems and nanostructures, e.g., quantum Hall effect, microwave induced magnetoresistance oscillations, quantum corrections to conductivity, edge state transport in topological insulators, wave function multifractality at Anderson transitions, many body localization, etc. 
This vast body of knowledge is not covered by standard MIPT courses. However, understanding of the above mentioned phenomena is necessary ingredient for successful work (both experimental and theoretical) in the field of modern condensed matter physics. To fill this gap the lecture course is concentrated on the following topics:
  • quantum phenomena in electron transport in 2D systems with perpendicular magnetic field;
  • quantum phenomena in electron transport in low-dimensional systems at low temperatures;
  • Anderson transitions;
  • equilibrium and nonequilibrium superconductivity in nanostructures.
The presentation of the material is on the semi-qualitative level that makes the course to be accessible for students of different training level. The course is supplemented by the set of 30 problems.

Preliminary syllabus:
  1. Quantum phenomena in electronic transport in two-dimensional systems in magnetic field.
    • Lecture 1. Kinds of disorder in two-dimensional systems.Quantum and transport time. Landau level broadening by disorder. Oscillations of density of states in magnetic field. De Haas - Van Alphen and Shubnikov - De Haas oscillations. AC conductivity oscillations. Cyclotron resonance and its harmonics.
    • Lecture 2. Microwave radiation induced conductivity oscillations. Zero resistance state. Current dimain decomposition. Microwave radiation induced photovoltaic effects.
  2. Quantum phenomena in electronic transport in low-dimensional systems at low temperatures.
    • Lecture 3. Polarization functional under diffusion approximation. Dynamic and static screening of interelectronic interaction. Density of states suppression at the Fermi level. Diffusons and cooperons. Weak localization and antilocalization.
    • Lecture 4. Phase fault time. Conductivity temperature dependence at low temperatures. Altshuler-Aronov correction to the conductivity. Scattering by Friedel oscillations. Magnetoresistance.
    • Lecture 5. Ginzburg-Landau functional. Superconductivity in pellets. Levanyuk-Ginzburg criterium. Lifetime of fluctuation pairs. Ginzburg-Landau temporal equation. Fluctuation corrections to the density of states. Conductivity temperature dependence near superconducting state transition: paraconductivity, Maki-Thompson correction. Magnetoconductivity.
  3. Anderson transitions in disordered electronic systems.
  4. Equilibrium and non-equilibrium superconductivity in nanostructures.

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  2. I.A. Dmitriev, A.D. Mirlin, D.G. Polyakov, M.A. Zudov, Nonequilibrium phenomena in high Landau levels, Review of Modern Physics 84, 1709 (2012).
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  6. A.D. Mirlin,  F. Evers, I.V. Gornyi, P.M. Ostrovsky, Anderson transitions: Criticality, symmetries and topologies, International Journal of Modern Physics B 24, 1577 (2010).
  7. A.P. Schnyder, S.Ryu, A. Furusaki, A.W.W.Ludwig, Classi?cation of Topological Insulators and Superconductors, AIP Conference Proceedings 1134, 10 (2009).
  8. A. Kitaev, Periodic table for topological insulators and superconductors, AIP Conference Proceedings 1134, 22 (2009).   
  9. A. Punnoose, A.M. Finkelstein, Metal-insulator transitions in disorderd two-dimensional electron systems, Science 310, 289 (2005).
  10. K.Yu. Arutyunov, D.S. Golubev, A.D. Zaikin, Superconductivity in one dimension, Physics Reports 464, 1 (2008).
  11. R. Fazio, H. van der Zant, Quantum phase transitions and vortex dynamics in superconducting networks, Physics Reports 355, 235 (2001).

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