The course is offered in a 10-ECTS version (Solid State Physics), to which two 5-ECTS courses (Solid State Physics A and Solid State Physics B) are offered jointly. The present detailed program defines aims, educational outcomes and syllabus for every joint course.

Solid State Physics (10 ECTS)

The course goals are the union of those of part A and part B as follows:

Solid State Physics A (5 ECTS)

The course aims at giving students the fundamentals of solid state physics at a graduate level. Long range order solids (crystals), their structural properties (symmetry) and static electronic structure are of main concern. After an introduction to crystallography, the main experimental tools used to determine the geometric structure of crystals are discussed together with the related theory. Then quantum mechanics is used to find the electronic band structure both introducing the general properties of electronic states in a periodic potential and presenting the main approximate methods  to calculate the energy levels. At last the effect of an external static field is studied by means of crucial concepts like: density of states, equivalent Hamiltonian, effective mass, semiclassical dynamics and electron-hole representation. All arguments are illustrated by examples.

Solid State Physics B (5 ECTS)

The course aims at giving students the basic principles for the approximate solution of the many body Schroedinger equation for a crystal at a finite temperature including lattice vibrations: Born-Oppenheimer and mean-field approximations. Classical lattice dynamics is then introduced (interatomic force constants and dynamic matrix, lattice waves with their frequencies and polarization) and eventually quantized presenting the new concepts of acoustic and optic phonons. On this basis thermodynamic properties like specific heat and thermal dilation are made microscopically understandable. Always using quantum mechanics the macroscopic optical properties of crystals are derived from a microscopic treatment of electronic transitions. At the end transport properties (electrical and thermal conductivities and their temperature dependence) are introduced and explained in terms of physical kinetics. All arguments are illustrated by examples.

Solid State Physics (10 ECTS)

The expected learning outcomes are both those of part A and of part B, as detailed in the following.

Solid State Physics A (5 ECTS)

The student:

• knows the mathematics and the physical principles required to understand what is a solid body and, in particular, a crystal together with the geometric structure of the most important crystals.
• knows the main quantities defining the crystalline state, together with the theoretical models and experimental methods suitable to describe it and to ascertain its structure, with particular reference to perfect “frozen” periodic lattices with a basis of atoms.
• is able to forecast the main static electronic properties (band structure) of specific crystals knowing the fundamentals of the quantum mechanics of one electron in a periodic potential and the main approximate methods to compute the band structure itself.
• is able to exploit the above theoretical models to develop the description of the accelerated motion of an electron in a specific crystal subjected also to a static external field using the electron-hole representation.

Solid State Physics B (5 ECTS) 

The student:

• knows the theoretical models required to approximately solve the many body Schroedinger equation for a crystal including nuclear vibrations.
• knows the fundamentals of both classical and quantum lattice dynamics (lattice waves and phonons).
• is able to apply quantum mechanics to understand and forecast the macroscopic thermodynamic and optical properties of specific crystals.
• is able to apply quantum mechanics and physical kinetics to understand and forecast the macroscopic transport properties (electrical and thermal conductivities) of specific crystals.

Solid State Physics (10 ECTS)

The topics of this course are both those of part A and part B as listed in the following.

Solid State Physics A (5 ECTS)

Solid bodies Order and symmetry, simple crystals: lattices and translational order, reciprocal lattice, complex crystals: lattice and basis,  crystal binding, tensorial observables.

Scattering theory Quantum particle scattering amplitude: Born approximation, Elastic scattering - Bragg law, X-Ray Diffraction.

Electronic States Bloch’s Theorem, reduction to the first Brillouin zone and periodic boundary conditions, free electron model (Fermi energy and density of states), band structure: nearly free electron approximation, band structure: tight binding and LCAO approximations. General way to compute the density of states.

Electron dynamics in external fields: equivalent Hamiltonian,  effective mass theorem, impurity levels, semiclassical dynamics in an ideal crystal, electric current and Bloch oscillations, electrons and holes, excitons.

Solid State Physics B (5 ECTS)

Adiabatic theorem and vibrational motions

Lattice dynamics Lattice specific heat: Einstein model, simple 1D crystal: lattice waves and acoustic phonons, linear chain with two atoms per cell: acoustic modes and optical modes, general 3D lattice dynamics: interatomic force constant tensor and dynamic matrix, phonons in a 3D complex crystal, Debye model of specific heat, thermal dilation and anharmonic processes, polaritons.

Optical properties Macroscopic description of dispersion and absorption of photons, Kramers and Kronig relations for the frequency dependent dielectric susceptibility, quantum treatment of photons absorption, optical properties of direct band gap semiconductors, the case of indirect band gap, optical properties of polaritons.

Transport phenomena Local Ohm law and Fourier law, experimental temperature dependence of electrical and thermal conductivities, physical kinetics and Boltzman equation, microscopic theories of electrical conductivity and of thermal conductivity of metals, microscopic theory of thermal conductivity of insulators (phonon-phonon scattering).

To attend the course a knowledge, at least at an elementary level, of calculus, classical mechanics, thermodynamics, electromagnetism and quantum mechanics is required. To attend Solid State Physics B a knowledge of the subjects contained in the programme of Solid State Physics A is assumed.

The evaluation consists in an oral examination. It aims at verifying both the knowledge and the understanding of the course topics and also the ability to apply critically this general knowledge to develop the description of: (Solid State Physics A) main quantities defining specific crystals, theoretical electronic band structure models for specific crystals, ideal response of crystal electrons to external static fields; (Solid State Physics B) electron-phonon approximate decoupling, vibrational (phonon) properties, thermodynamic and optical properties of specific crystals. Transport properties of specific crystals.

The knowledge of the systems of units, the value of the fundamentals physical quantities in Solid State Physics, the structure of the most important crystals and their main properties are addressed as well for both part A and B.