Electron transport in quantum systems
Lectures (spring 2018)
- (22.02.) Low-dimensional systems, 2DEGs in semiconductor
heterostructures and other systems. Overview
of topics covered by the lecture.
Quantum-mechanical (single-particle) description in the
envelope function approximation. Self-consistent calculations of
heterostructure parameters. Mobility and mean free path.
Examples of low-dimensional systems.
- (01.03.; lecture given by Jakub Zelezny) Quantisation of
conductance in quasi-1D conductor,
Landauer formula. Transmission coefficient (simple example and
more realistic structures). Calculations for spintronic structures
using kwant (such as
MTJ to be discussed latter in this course).
- (15.03.) Contact resistance (in connection to Landauer formula).
Double barrier as a basis for the model of 1D disordered wire. Its
modification for finite coherence length (nonzero temperature) and
weak localisation. Aharonov-Bohm experiment.
Slides.
- (22.03.) Weak localisation in various dimensions. Strong localisation
(Anderson transition, percolation picture). Effect of magnetic field,
note the Hikami-Larkin-Nagaoka formula on
slides. Scaling approach. Models of metal-insulator transition:
clean crystal (1D tight-binding), Anderson (disorder), Mott
(electron-electron interactions).
- (27.03.) Demonstration of the simple model exhibiting the
Anderson transition. Quantum effects on thermopower in quasi-1D channels.
Slides.
- (11.04.) Drift and diffusion. Derivation of Drude conductivity
within classical, semiclassical and fully quantum-mechanical framework.
- (19.04.) Kubo formula (DC and AC conductivity). Description of
scattering in quantum-mechanical (selfenergy) and semiclassical
framework (Fermi golden rule). Quantum lifetime and transport lifetime.
Semiclassical approach to thermoelectric
phenomena (plus discussion of Seebeck coefficient, figure of merit and
Wiedemann-Franz law). Conductivity tensor in non-zero magnetic field.
Slides.
- (26.04.) Semiclassical derivation of the conductivity tensor in
non-zero magnetic field (Chamber's solution of the Boltzmann equation,
semiclassical dynamics). Magnetoresistance of a two-component electron
gas (semimetals). Shubnikov-de Haas oscillations, measuring the
Fermi surface in 3D by applying magnetic field in various directions.
Slides.
- (03.05.) 2DEG subject to magnetic field (Landau levels, filling
factor). Integer quantum Hall effect (edge states, percolation picture,
localised/delocalised states). Fractional quantum Hall effect.
Slides.
- (10.05.; lecture given by Richard Korytar) Transport
through molecular junctions (brief intro into experiments, comparison
to quantum dots). Derivation of the formula for current using
Green's functions. Resonant tunneling through single level as an
example.
- (17.05.; lecture given by Richard Korytar) Coulomb
blockade for tunneling through a molecule: Anderson impurity model,
Kondo effect.
- (18.05.) Kondo effect (in metals with magnetic impurities). Tunneling
through QDs: single level spectroscopy, Coulomb blockade. Role of
spin in transport: Hanle effect (spin precession explained).
Slides.
- (29.05.) Bonus lecture: more on spin effects. GMR and T(A)MR
(magnetoresistance in multilayers). Anisotropic magnetoresistance.
Anomalous Hall effect. Spin Hall effect (SHE) and quantum SHE.
Lecture notes ('skriptum'
by Pavel Streda) and
addenda.