SOLID STATE PHYSICS
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- Versione italiana
- Academic year
- 2022/2023
- Teacher
- FEDERICO SPIZZO
- Credits
- 6
- Didactic period
- Primo Semestre
- SSD
- FIS/03
Training objectives
- The course presents some of the models developed for the comprehension of the properties of crystalline solids, highlighting the hypotheses that represent the starting point for the models, the results that can be obtained using those models and the comparison between these results and the experimental behavior of the solids.
The aim of the lessons is to show how some of the properties of the solids, e.g. the electronic conductivity or the specific heat dependence on temperature, can be explained starting from some base hypotheses, so to provide some interpretative schemes that may be useful in view of future studies concerning the properties of solids.
The main acquired knowledge will be: electronic conductivity and dielectric constant features in the Drude approximation; how the properties of the electrons change when switching from the classical approach to the quantum mechanical approach; electronic conductivity, dielectric constant and optical properties of a solid when the electron – lattice interaction is considered; effect of the electron-electron interaction on the properties of solids; effect of lattice vibrations on the electronic and optical properties of solids.
The basic acquired abilities will be: the knowledge of the methods that can be used to develop a description of the microscopic and macroscopic properties of a solid; the capability to understand the correlation between the properties of a solid and the features of the solid at the microscopic level. Prerequisites
- The following concepts are mandatory:
main concepts regarding solid state that are presented during the “Struttura della Materia” (Structure of Matter) course of the Bachelor Degree;
basic knowledge of quantum mechanics;
Fermi-Dirac and Bose-Einstein distribution;
features of the main crystalline lattices;
direct lattice, reciprocal lattice. Course programme
- Classical approach applied to free and independent electrons in solids (10 hours): Drude model, electronic conductivity, dielectric constant, Hall effect and magnetoresistance.
Quantum mechanical approach to free and independent electrons in solids: Sommerfeld model.
Interactions between independent electrons and the crystalline lattice periodic potential (20 hours):
Bloch theorem;
free electrons in a small periodic potential;
effects of the periodic potential on the shape of the Fermi Surface;
electronic bands in solids;
methods used to evaluate the electron band structure in solids: tight-binding; OPW; Pseudopotential.
semiclassical model.
Fermi Surface and electronic bands description for selected metals. Experimental methods for the investigation of the shape of the Fermi Surface.
Electron-electron interaction (10 hours):
Hartree model;
Hartree-Fock model, Slater determinant: exchange term. Electronic contribution to the permittivity of the solid.
second quantization formalism applied to fermions: effect of electron-electron interactions in terms of creation and destruction operators.
Effect of electron-electron interaction on the energy levels; Fermi liquid.
Lattice vibrations (14 hours):
three dimensional crystalline lattice;
normal model of oscillation, phonons;
specific heat dependence on temperature;
electron-phonon interaction;
electrical resistivity dependence on temperature;
umklapp processes.
Permittivity of solids:
phonons contribution to the dielectric constant given; evaluation of the solid permittivity; effective potential ruling electron-electron interaction.
Superconductivity:
overview;
electrons binding energy following the Cooper method. Didactic methods
- The course is organized as frontal lessons on all course topics.
Learning assessment procedures
- The aim of the oral examination is to verify if the training objectives have been achieved and to evaluate if the student has performed a critical analysis of the presented topics.
The first topic of the oral examination can be chosen by the student, who has at disposal about 10-15 minutes to present that; this topic can be selected among those presented during the lessons. The aim of this initial presentation is to verify if the student can explain in a detailed way the chosen topic and develop a proper arrangement of the sub-topics that are needed during the discussion. After the presentation of this first topic, the oral examination proceeds with the discussion about the other subjects presented during the lessons. Reference texts
- N. W. Ashcroft e N. D. Mermin "Solid State Physics" (Saunders College, Philadelphia, 1976) o (CBS, international, 1988).
