Physics of solids 1

A.Y. 2020/2021
6
Max ECTS
42
Overall hours
SSD
FIS/03
Language
Italian
Learning objectives
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.
Course syllabus and organization

Single session

Responsible
Lesson period
Second semester
In case of travel restrictions due to Covid-19, the course will be fully delivered through remote teaching.
In this case, the lectures will be offered in virtual classrooms (zoom platform) in synchronous connection, with the possibility of real-time interaction between the students and the teacher.
Course syllabus
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. Electron-electron correlation effects and electron-phonon effects. Excitons, plasmons, polaritons, polarons, superconductivity (brief).
Prerequisites for admission
Basic mechanics, thermoyinamics, statistics, electromagnetism, quantum mechanics, and structure of matter.
Teaching methods
Lectures. The topics are discussed verbally and through illustrations and equations at the blackboard.
Specific contents such as tables and illustrations are provided in paper and electronic format.
For selected topics, flipped classes are implemented: students learn the subjects on textbooks, and then the lecture consists of a discussion guided by the students themselves.
Teaching Resources
- C.Kittel, Introduction to Solid State Physics (Wiley New York 1996)

- J.R. Hook and H.E. Hall, Solid State Physics (Wiley Chichester 1991)

- G. Grosso and G. Pastori Parravicini, Solid State Physics (Academic, San Diego, 2000)

- N.W. Ashcroft and N.D. Mermin, Solid State Physics (Holt Sanders NY 1976)

- J.M. Ziman, Principes of the theory of solids (Cambridge University Press 1972)

- J.Callaway, Quantum Theory of the Solid State (Academic 1991)
Assessment methods and Criteria
Oral exam: a few course topics are discussed for 45-60 minutes.
The exam will gauge the student's acquired competences and critical skills, through the discussion of problems in solid-state physics.
FIS/03 - PHYSICS OF MATTER - University credits: 6
Lessons: 42 hours
Professor: Manini Nicola
Professor(s)
Reception:
Tuesdays 2pm - 5pm
office, via Celoria 16, room A/T/C11