Introduction to Modern Solid State Theory
Priv. Doz. Dr. Mikhail Kiselev
4 hours per week (in English or German)
This lecture course is proposed for the students starting from 6 Semester, interested in a Diploma Project in theoretical physics. This course gives an introduction to modern theoretical condensed matter physics, including the theory of strongly correlated systems (heavy fermions, high-temperature superconductors, quantum Hall effect, optical lattices). The emphasis will be given to the theory of cooperative phenomena (magnetism, superconductivity etc). The course will be useful for students interested in theory of strongly correlated phenomena and phase transitions.
Tentative plan for the lectures:
o Theory of crystals: Lattices.
Periodicity.
o
Electrons
in a lattice:
Electron
in periodic potential.
Tight-binding approximation. The model
of near free electrons. Main properties of Bloch electrons (effective mass etc). Statistics of electrons in solids.
Basics of theory of metals. Fermi liquid. Electron-phonon interaction. Polarons.
o
Statistics and
thermodynamics: Specific heat of crystal lattices.
Specific heat of the electron system.
Magnetic properties of the electron gas. Pauli Paramagnetism. Landau Diamagnetism. de
Haas- van Alphen effect.
o
Electrodynamics of
metals: Skin effect. Anomaly skin effect.
Cyclotron resonance. Quantum oscillations. Weak localization.
o
Transport in metals: The Boltzmann equation for electrons.
Conductivity and thermoelectric phenomena. Electron-electron scattering. Shubnikov-de Haas effect. Hall effect.
o
Semiconductors: Basic concepts. Intra-band transitions. Excitons.
Doped semiconductors. Impurity states. Localization of
electron states. Charge and Spin Density Waves.
o
Phase Transitions: First order phase transitions.
Second order
phase transitions. Ginzburg-Landau functional.
Scaling. Fluctuations. Critical phenomena. Quantum Phase
Transitions.
o
Bose Gases: Ideal Bose Gas. Bose-Einstein Condensation. Effects of interaction. Superfluidity. Vortices. Thermodynamics
of Bose Gas. Optical lattices. Supersolids.
o
Superconductivity: Fundamental properties. Phenomenology. Ginzburg-Landau equations. Josephson effect. Basic concepts
of microscopic theory: Cooper pairing, BCS
equations.
o
Magnetism: Local moments. Ising model. Heisenberg model Ferromagnets and Antiferromagnets. Magnons. Spin
correlation functions. Itinerant magnetism. Stoner
model. Spin waves. Thermodynamics of spin waves.
o
Strongly correlated
electrons: Hubbard model.
Recommended literature:
1)
N.W.Ashkroft and N.D. Mermin. Solid State Physics. (Holt, Rinehart and
Winston, New York 1976)
2)
C.Kittel.
Quantum Theory of Solids.(John Wiley and Sons, New York 1987)
3)
J. M. Ziman. Principles of the Theory of Solids. (Cambridge
University Press,
Cambridge, 1979)
4)
A. Abrikosov. Fundamentals of the Theory of Metals
(North-Holland,
Amsterdam, 1988)
5)
R. White. Quantum Theory of Magnetism.
(Springer-Verlag, 1983)
6)
A. Auerbach. Interacting Electrons and Quantum Magnetism.
(Springer-Verlag,
1994)
7)
G.Mahan,
Many-Particle Physics (Plenum press, NY 1993)