Introduction to Modern Solid State Theory

 

Lecture # 1                   13.04.05

 

Introduction. Modern Solid State Physics: problems, methods, perspectives.

 

Lecture # 2                   15.04.05

 

Electron in a crystal lattice. Bloch theorem. Born-von Carmann boundary conditions. Reciprocal lattice.

Model 1: near free electrons. Model 2: tight binding approximation.

 

Lecture # 3                   18.04.05

 

Ideal Fermi and Bose gases. Symmetry, spin and statistics. Thermodynamic potentials. Distribution functions.

Fermi sphere. Fermi momentum. Effective mass. Band structure. Classification of materials depending on the band filling.

 

Lecture # 4                   20.04.05

 

Fermi liquid. Quasiparticles.  Excitations in Fermi gas. From Fermi gas to Fermi liquid. Lifetime. Electron specific heat of Fermi liquid. Experimental verification of Fermi liquid properties.

 

Lecture # 5                   25.04.05

 

Lattice vibrations. Phonons. Interactions between atoms in solids. One atomic linear chain. Acoustic phonons. Diatomic linear chain. Optic phonons. Group and phase velocities.

 

Lecture # 6                   27.04.05

 

Classical and quantum oscillators. Lagrange and Hamilton approaches to oscillator problem. Matrix elements. Schrödinger equation. Electron in a magnetic field (energies). Canonical variables. Second quantization for oscillators. Thermodynamics of oscillators.

 

Lecture # 7                   02.05.05

 

Magnetism of electronic systems. Spin. Pauli paramagnetism. Electron in magnetic field (level quantization). Landau levels. Degeneracy. Diamagnetism. Oscillations. De Haas –van Alphen effect.

 

Lecture # 8                   04.05.05

 

Transport in metals (I). Electron in electric and magnetic fields (classical description). The Boltzmann equation for electrons. Collision integral. Impurity scattering. The transport relaxation time. Mean free path. Drude conductivity. Diffusion coefficient. Einstein relation.

 

Lecture # 9                   09.05.05

 

Transport in metals (II). Thermoelectric phenomena. Thermocouple. Seebeck effect. Peltier effect. Onsager symmetry relations. Scattering mechanisms (electrons, lattice vibrations, impurities).

 

Lecture # 10                 11.05.05

 

Magnetic correlations. Magnetic impurities in non-magnetic metals. Kondo effect. Calculation of resistivity.  Kondo effect in quantum dots. RKKY interaction. Oscillation of exchange integral. Magnetic orderings. Spin glasses.

 

Lecture # 11                 18.05.05

 

Phase transitions theory. Examples of phase transitions. Classification of phase transitions. Phase transitions of 1st order.  Landau theory of 2nd order phase transitions. Critical exponents. Fluctuation correction to specific heat. Ornstein-Zernike theory. Ginzburg number. Scaling equations.

 

Lecture # 12                 23.05.05

 

Second quantization. Schrödinger and Heisenberg equations. Symmetry of many particle wave function for non-interacting systems. Symmetric wave functions: bosons. Slater determinant: fermions. Bose and Fermi commutation relations. Pairwise interactions.

 

Lecture # 13                 25.05.05

 

Bose Gas (I). Bose Einstein Condensation. Ideal Bose gas. BEC. De Broglie wavelength. Thermodynamics of Bose gas. Coherence. Weakly Interacting Bose Gas. Bogolubov transformations. Excitations. Experiments in dilute Bose gases. Ultra cold gases of alkali metals.

 

Lecture # 14                 30.05.05

 

Bose Gas (II). Superfluidity. Phonons in interacting Bose gas. Landau criterion. Correlation functions in Bose gas. Condensate wave function. Quantization of vortices. Two-component hydrodynamics. Experiments in superfluids.

 

 

Lecture # 15                 01.06.05

 

Superconductivity (I).  Phenomenology of superconductivity.  Meissner effect. Londons equations. Isotopic effect. Frölich Hamiltonian. Attraction between electrons due to electron-phonon interaction. Cooper pairing.

 

 

Lecture # 16                 06.06.05

 

Superconductivity (II). Microscopic Theory of Superconductivity. Gap equation. Thermodynamics of superconductors.

 

 

Lecture # 17                 08.06.05

 

Superconductivity (III). Ginzburg-Landau theory. Electrodynamics of superconductors. Josephson effect.

 

 

Lecture # 18                 13.06.05

 

Magnetism (I). Local moments. Classical theory of magnetism. Langevin function. Quantum theory of magnetism. Brillouin function. Heisenberg model. Ferromagnets and Antiferromagnets.

 

 

Lecture # 19                 17.06.05 *)

 

Magnetism (II). Spin waves in ferromagnets and antiferromagnets. Magnons. Thermodynamics and magnetization. Ising model. XY model. Kosterlitz-Thouless transition.

 

Lecture # 20                 20.06.05 **)

 

Fermi Surfaces. Electronic Topological Transition.

 

 

Lecture # 21                 22.06.05

 

Magnetism (III).  Bloch equations. Magnons in FM and AFM. Itinerant magnetism. Stoner criterion. Spin waves in itinerant ferromagnets. Spin density waves. Hubbard model. Correlation effects.

 

 

Lecture # 22                 27.06.05 ***)

 

Geometry of  lattices. Bravais lattices in 2D and 3D. The Wigner-Zeitz cell. X-Ray diffraction in periodic structures. Experimental methods of diffraction.

 

Lecture # 23                 29.06.05 ***)

                                     

Electrodynamics of metals. Cyclotron resonance. Hall effect. Skin effect. Anomaly skin effect.

 

Lecture # 24                 04.07.05

 

Coulomb interaction in metals. Dielectric function. Plasmons. Friedel oscillations.

 

 

Lecture # 25                 06.07.05

 

Strong correlations (I). High temperature superconductivity. Hubbard model. Anderson model. t-J model. d-wave superconductivity. Metal-Insulator transition.

 

 

Lecture # 26                 11.07.05

 

Strong correlations (II). Heavy fermions. Interplay between on-site and inter-site correlations. Kondo lattices. Quantum phase transitions.

 

 

Lecture # 27                 13.07.05

 

Strong correlations (III).  Symmetries in solid state physics. Hidden symmetries. Hidden orders. Dynamical symmetries.

 

 

*) Lecture on 15.06.05 is shifted to 17.06.05 (09:30 Theresienstr. 37, Room 449)

 

**) Lecture on 20.06.05 is cancelled due to my absence. Materials will be delivered as printouts.

 

***) Lectures on 27.06.05 and 29.06.05 are cancelled due to my absence. Materials for cancelled lectures will be delivered as printouts.