This course targets a general understanding of a broad range of fundamental phenomena and properties of solid-state matter. The course covers electronic, vibrational, and spectroscopic properties of crystals, plus heat and electricity transport
Expected learning outcomes
The student is expected to learn in detail:
1. Periodic crystals and crystal lattice. Direct and reciprocal lattice. X-ray diffraction. Miller indices. Form factor and structure factor. Packing fraction. Quasicrystals (brief).
2. Total cohesive energy of the crystals. Simple examples of crystals of noble gases and ionic solids. The density functional theory (DFT) for calculating total adiabatic energy of a solid. Similarities and differences with Hartree-Fock. Approximate density functionals: the Thomas-Fermi and Kohn-Sham methods; the local density approximation (LDA).
3. Linear elastic response and the elastic constants of a solid.
4. Atomic motions in a crystalline solid: the harmonic approximation, lattice vibrations and phonons. Phonon dispersions in special directions of cubic crystals: longitudinal modes and transverse modes. Phonons in 3-dimensional solids in arbitrary crystal directions. The LO-TO splitting in cubic crystals.
5. Methods for measuring the dispersion curves of phononic frequencies. Brief review of the thermal properties of phonons, the Debye model.
6. Anharmonic effects in crystals: the Gruneisen theory of the thermal expansion of solids, collisions between phonons, thermal conductivity.
7. A simplified model for the motion of electrons in metallic solids: the jellium model, and its DFT solutions. Charge and heat conduction in the relaxation-time approximation. Hall coefficient.
8. Band theory of solids: electrons in a periodic potential, models and methods for the calculation of the electronic bands (brief). General features of the structural and electronic band calculations of crystals within the DFT approach. Semiclassical motion of the electrons in crystals, effective mass. Holes and their motion.
9. Semiconductors: the valence and conduction bands, intrinsic and doped semiconductors, carriers, mobility, conductivity, Hall effect, cyclotron resonance. A few transport and out-of-equilibrium effects. The p-n junction. A panorama of inhomogeneous semiconductor applications.
10. Metals: AC response and conductivity. The Boltzmann equation. Optical response of the electrons and spectroscopies. Out-of-equilibrium and thermoelectric effects.
11. Elements of electron-electron correlation effects and screening effects. Excitonic effects: optical gap and quasiparticle gap. Optical excitations: plasmons, polarons.
Lesson period: Second semester
(In case of multiple editions, please check the period, as it may vary)