Syllabus - a.a. 2018/2019
In this page, the topics discussed during each lesson are presented.
September, 24
Introduction to the Solid State Physics Course. The Drude model for the description of metallic solids: hypotheses of the model, relaxation time. Effect of electronic collisions on the equation of motion of the electrons; DC conductivity, Hall coefficient. [AM]
September, 25
AC conductivity; calculation of the dielectric permittivity. Optical properties of the Drude metal. Evaluation of the electronic contribution to the specific heat of the metal. Introduction to the Sommerfeld model; Schrodinger equation for the free electron. Quantization of the electronic wavevector. [AM]
October, 1
Fermi energy and Fermi surface, average value of the electronic energy, electronic energy density. Optical properties: hints; specific heat of the free electron gas. Failures of the free and independent electron Sommerfeld model; removal of the free electron approximation. [AM]
October, 2
Bloch theorem; general expression for the electronic wavefunction; Born-Von Karman periodic boundary conditions. Electronic wavefunction periodicity in the direct and in the reciprocal space. Demonstration of the Bloch theorem. Electron velocity. The case of the null potential case. [AM]
October, 8
The case of a small potential: its effect on the energy of the electronic levels both in the non-degenerate and in the degenerate case. Bragg planes. Bragg planes and how they affect the shape of the Fermi surface. [AM]
October, 9
Energy vs. wavevector dependence for core electrons: the tight binding model; general solution and its application to the case of s orbitals. Combination of core electrons and valence electrons: the orthogonalized plane-wave method; the pseudopotential. [AM]
October, 15
Introduction to the semiclassical model: main hypotheses and equation of motion for the electron. Contribution to conductivity given by filled/partially filled/empty bands; distinction between metals, semiconductors and insulators. The effect of a DC electric field. Effective mass and effective mass tensor. [AM]
October, 16
Electrons orbits in presence of a DC magnetic field: open orbits and closed orbits. Electron trajectory in presence of mutually perpendicular electric and magnetic fields: Hall effect and magnetoresistance. [AM]
October, 22
Conductivity tensor for Bloch electrons in presence of a DC electric field. Methods for the determination of indications about the shape/structure of the Fermi Surface: the De Haas-Van Alphen effect. Landau levels. [AM]
October, 23
Explanation of the De Haas-Van Alphen Effect. Ratio between Fermi wavevector and size of the Brillouin zone for fcc and bcc lattices: the case of alkali metals and noble metals. General structure of the Fermi Surface. [AM]
October, 29
Effect of the electron-electron interaction: Hartree method; Hartree-Fock method. Slater determinant. Expectation values for 1-body and 2-body operators. [AM/pdf document for the Slater Determinant]
October 30
Energy variation due to the electron-electron interaction: direct term and exchange term. Calculation of the exchange energy contribution for the case of free electrons. Electronic contribution to the dielectric constant. Introduction to the second quantization formalism.
November, 5
Representation of 1-body and 2-body operators using the second quantization formalism. Calculation of the energy contribution due to electron-electron interaction: direct term and exchange term.
November, 6
Effect of the ionic oscillations in the harmonic approximation. Dynamical matrix; general properties of the eigenvalues and eigenvectors of the dynamical matrix.
November, 12
Hamiltonian of the 3D lattice as a combination of normal mode contributions; from the classical picture to the quantum mechanical one. Phonons. Hamiltonian of the 3D lattice as a combination of quantum mechanical harmonic oscillators; creation and destruction operators. Evaluation of the specific heat in the low temperature and high temperature approximations.
November, 13
Specific heat evaluation: Debye approach. Debye wavevector and Debye temperature. Einstein model. Electron-phonon interaction: evaluation of the effects and of the electron-phonon coupling using the second quantization formalism.
November, 19
Effects of the electron-phonon interaction: resistivity. Evaluation of the resistivity dependence on temperature: high temperature and low temperature regimes. Normal and Umklapp processes. Energy and momentum conservation laws. Electron-photon interaction in presence of phonons: direct and indirect transitions.
November, 14
[AM] N. W. Ashcroft - D. Mermin, Solid State Physics
