qtr

Weekly log

Topics covered in individual lectures:

• (21.02.) Low-dimensional systems, envelope-function approximation (EFA). Slides.
• (28.02.) Tight-binding model (1D chain) as an example for idea behind EFA. Drude formula (classical formalism). Concept of semiclassical description of transport.
• (07.03.) Quantum-mechanical derivation of conductivity (Kubo formula), scattering quantified by Fermi golden rule or selfenergy. Slides and references. Kubo formula is derived as Eq. 1.26 at the beginning of diploma thesis of J. Kolorenč.
• (14.03.) Jakub Železný: Landauer formula, quantum point contacts. Magnetic tunnel junctions (MTJ), giant magnetoresistance (GMR), calculations using kwant. Slides.
• (21.03.) Localisation at zero temperature (exponential resistance). Coherence length. Aharonov-Bohm effect. Slides and references.
• (28.03.) shared with Jakub Zázvorka: Weak localisation. Universal conductance fluctuations. Metal-insulator transitions (Anderson type, Mott type). Shot noise. Introduction to magnetoresistances (MRs): resistivity tensor, classical Hall effect. Geometrical MR.
• (04.04.) Jakub Zázvorka: two-band MR (and the common positive MR in metals), comments on systems with closed and open Fermi surfaces. 2DEG subject to magnetic field (Landau levels, filling factor). Quantum Hall effect (QHE). Slides
• (11.04.) Localised and delocalised states in the QHE (mobility edge). Slides of JZ Transition to Shubnikov-de Haas oscillations and their semiclassical explanation. Berry phase for an electron following its cyclotron orbit. Introduction to the fractional QHE. Slides of KV and references.
• (25.04.) Examples of what role electron spin can play in transport. Spin precession in vacuum and in non-local spin valves (Hanle effect). Spin-orbit interaction obtained perturbatively from the Dirac equation. Edelstein effect. Adiabatic theorem. Slides and references.
• (02.05.) Berry phase (general derivation and an example of correction to semiclassical treatment of electrons in magnetic field). Effective Hamiltonian for graphene. Tunneling through quantum dots (QDs). Spectroscopy of QD levels. Josephson effect (tunneling between two superconductors). Slides.
• (09.05.) Richard Korytár: What are molecular junctions? Brief intro into experiments. Energy scales and length scales of electronic and vibrational excitations. Coherent quantum transport of electrons. Scattering theory revisited. Derivation of the formula for the transmission probability. The Green’s function: a simple example. Resonant level. The electric current (formula). Applications: current in the scanning-tunneling microscope.
• (15.05.) Richard Korytár: Single and two-orbital molecular junctions. Quantum interference causes Fano resonances. Coulomb blockade in a single impurity Anderson model. Atomic limit. Suppression of transmission. Kondo effect.
• (30.05.) Bonus lecture. Microscopic wavefunction of the BCS (Bardeen-Cooper-Schrieffer) superconducting state. Laughlin state (fractional QHE, filling factor 1/3) as another example of a many-body wavefunction. A quick overview: spin Hall effect (SHE) and quantum SHE, anomalous Hall effect, anisotropic magnetoresistance (AMR), tunneling AMR. Coulomb blockade in QDs. Slides and references.