Syllabus

Introduction (12 hours):

interactions in condensed matter (gas, liquid, crystal), conductivity of metals (Drude model), charge screening in metals and plasma, diffusion and mob il ity (Einstein relation), conductivity in magnetic field (Drude model), translational symmetry (Bloch theorem) energy bands and quasi-momentum, almost free electrons model, tight binding model, density of states, acoustic and optical phonons, secondary quantization, quasi-particles, low energy spectra in condensed matter (Landau approach), phonon modes localized on lattice defects.

Part I (12 hours):

Semi-classical dynamics of electrons in metals in electric and magnetic fields, Fermi-surface of electrons in metals, closed and open trajectories, Landau quantization in metals, density of states in magnetic field, Boltzmann equation (t-approximation), electrical and thermal conductivities, Onsager rules, thermoelectric phenomena, normal and anomalous skin-effect, ineffectiveness concept, Boltzmann equation for resonance phenomena, Azbel-Kaner resonance, collisionless plasma, plasma frequency, longitudinal permittivity and waves, Landau damping.

Part II (8 hours):

Magnetism of normal metals, paramagnetism Pauli, Landau diamagnetism, quantum osc il lations of magnetization (de Haas - van Alphen effect) and conductivity (Shubnikov – de Haas effect), ferromagnets and antiferromagnets, Weiss field, Courie point, Langevin equation, magnetization relaxation in ferromagnets, Lifshitz equation, spin waves in ferromagnets, ferromagnetic domains, spatial distribution of magnetization in domain walls in framework of Landau theory of second order phase transitions, surface tension of domain wall.

Part III (16 hours):

Electrodynamics of superconductors (London equation), field penetration depth, free energy of superconductors (London approximation), gauge invariant current density and flux quantization, Ginzburg-Landau equation, coherence length, surface tension of superconductor to normal states interface, proximity effect, Abrikosov vortex, energy of Abrikosov vortex, first critical field, Lorentz force, pinning force, conductivity of flux flow state, Josephson effect, long Josephson junctions, Josephson vortices, Josephson length and frequency, Cooper pairs, energy of Cooper pairs, Bogoliubov – de Gennes equations, Andreev reflection and quantization, BCS theory, self-consistence equation, pairing potential.

Part IV (6 hours):

Langevine equation, fluctuation-dissipation theorem (classical and quantum limits), sound wave in an ideal gas of phonons (second sound), Fokker – Planck equation (diffusion in momentum space).

Part V (6 hours):

Electron – electron interaction, structure of low energy spectrum of degenerate Fermi system, Fermi liquid, Landau theory of Fermi liquid, Landau f – function, susceptib il ity of Fermi liquid, spin waves in Fermi liquid.

Part VI (4 hours):

Nonlinear mechanics of a crystal, edge and screw dislocations, plastic flow of dislocations, energy of moving dislocations, size dependence of dislocation energy, shock wave in one dimensional crystal.

Textbooks

J. M. Ziman, ”Theory of Solids”, Cambridge, University Press, 1972.

A.A. Abrikosov, ”Fundamentals of the Theory of Metals”, New York, Academic, 1972.

M. Marder, ”Condensed Matter Physics”, New York, John W il ey, 2000.

Ne il W. Ashcroft and N. David Mermin, ”Solid State Physics”, New York, Saunders, 1976.

L. M. Sander, "Advanced Condensed Matter Physics", Cambridge, University Press, 2009.

P. M. Chaikin and T. C. Lubensky, "Principles of Condensed Matter Physics", Cambridge, University Press, 2010.