Syllabus
Progress in the semiconductor technology allows to prepare electron systems like two-dimensional electron gas, quantum wires and dots that can be much less than 100 nanometers in size. They are preferably prepared by combination of the electron lithography and the molecular beam epitaxy allowing controlled growth of atomic layers with the required atomic composition. Low-temperature properties of this new class of conductors cannot be explained on the basis of the classical physics. Wave-like properties of electrons giving rise the interference effects, size quantization of the energy spectra and the purely quantum property of the electron known as spin have to be taken into the consideration. The intensive study of these systems led to the discovery of the quantum Hall effects awarded by Nobel prizes in the years 1985 and 1998. Devices that relay on an electron's spin to perform their functions form the foundation of spin-based electronics, spintronics. The discovery in 1988 of the giant magnetoresistive eff ect is considered as its beginning. Also the superconductivity cannot be thought apart from quantum transport.
To explain the physical basis of the quantum transport of electrons by the simple way requiring the basic knowledge of quantum mechanical principles is the main aim of the course composed of the following topics: 1. Low-dimensional systems -- molecular beam epitaxy and lithography, quantum well design, size quantization, two-dimensional electron gas. 2. Electron transport as a scattering problem - conductance (= inverse resistance) and transmission coefficients, conductance quantization of the ballistic junction, Landauer-Büttiker formalism. 3. Localization and conductance fluctuations -- electron transmission through the two barriers in series, interference effect, localization length, universal conductance fluctuations. 4. Aharonov-Bohm effect -- quantization of the magnetic flux through the conducting loop. 5. Resonant tunneling and Coulomb blockade -- double-barrier tunneling, resonant and single electron tunneling, electron turnstile. 6. Integer quantum Hall effect -- energy spectra of electrons in strong magnetic fields, Landau levels and edge states, diamagnetic currents, localization effect. 7. Fractional quantum Hall effect -- incompressibility and filling factor, composite fermions. 8. Spintronics -- Zeeman splitting, giant magnetoresistance, spin-orbit coupling in semiconductor structures, spin precession, spin-polarized field--effect transistor. 9. Phenomenological theory of the superconductivity -- Bose-Einstein condensation, derivation of Ginzburg-Landau equations, critical currents and magnetic fields, diamagnetism. 10. Josephson effects -- tunnel junction, Josephson current, Shapiro staircase, voltage standard.
Annotation
Introduction to the electronic transport in mesoscopic systems including the following topics: conductance and transmission coefficients; localization, universal fluctuations and Aharonov-Bohm effect; quantum Hall effects; coherent resonant tunneling and Coulomb blockade; spin-dependent transport and spintronics; superconductivity and Josephson effects.