Corso di laurea magistrale Interateneo in Fisica dei sistemi complessi

1.Crystal structure and elettronic bands in solids  (16 hours)
The crystal and reciprocal lattice, main simmetry elements. X rays diffraction. The Von Laue theory and experimental techniques of diffraction. The geometrical structure factor and the atomic form factor.  Wigner-Seitz primitive cell. The Ewald construction.
The Drude model. Thermal and electrical conductivity of the electrons in a metal. The Hall effect and magnetoresistance. The Sommerfield model for the electrons in solids.
Electronic transport in a crystal lattice. Electrons in a weak periodic potential. Energy bands structure. The Bloch’s theorem and related general remarks. Energy levels near a single Bragg plane. Energy bands in one dimension. Methods for calculating band structure (short account).
The tight binding method. Semiclassical model for the electron dynamics in the energy bands, The effective mass and the effctive mass tensor.

2.Magnetic and superconductive properties  (16 hours)
The Spin Hamiltonian  in the  Heisenberg model. Magnetic interaction in a free elelctronic gas. The diamagnetic susceptibility. The paramagnetism. The equation of the Langevin’s paramagnetism and Curie law. The origin of the permanent magnetic moments of the electrons in a ferromagnetic solid. The ferromagnetic, antiferromagnetic, ferrimagnetic order, The Weiss’s molecular field. Electron exchange interaction, The magnetic domains. Bloch walls dinamic, the magnetic loss in a  cyclic magnetization regime. The phase transition from ferromagnetic to paramagnetic order. The Curie -Weiss law. The temperature dependence of the saturation’s  magnetization. Spin  waves and magnons.
Magnetic proiperties of a superconductor. The Meissner effect. Persistent surface  supercurrents. The magnetization curve. Critical parameters.Critical field. Type I and type II superconductors. Thermodinamics of the normal/superconductive transition. London ad Pippard equations. The flux quantization. DC and AC Josephson effect, application to the electrical metrology.

3.Statistical methods (16 hours)
Fundaments of statistical mechanics. Approximation methods. Variational principles, Fermionic systems. The Pauli paramagnetism.
The Ising model: definition, equivalence with other models. The binary law. Application to the order/disorder transformation in the metal alloys.
Spontaneous magnetization. The Bragg-Williams and the Bethe- Peierls transformation. Ising unidimensional model.
Critical phenomena, order parameters, correlation function, fluctuation-dissipation theorem. Critical exponents. Scale unvariance. Application to the study of the transition from the superconductive to the normal state of a superconductor.