Quantum theory of matter 2

A.Y. 2020/2021
Overall hours
Learning objectives
The course aims to introduce students to the physics of condensed matter and
its interaction with the electromagnetic radiation. The main topics addressed
are the electronic bands in solids, the magnetic behavior of the
matter with special attention to phenomena of magnetic ordering,
the phenomenology of superconductivity and the concept of quantum interference.
Furthermore, a part of the course is aimed at the study of the linear radiation-matter
interaction, at the description of the basic principles of laser action and the
properties of coherent radiation.
Expected learning outcomes
At the end of the course the student is expected to acquire the following knowledge:

1. The student will be able to describe the formation of the electronic band structure of solids;
2. He will be able to characterize experimental observations on the dynamics
of electrons in solids, both in electric fields and in magnetic fields;
3. He will be able to describe the magnetic behavior of the condensed matter, in particular
regarding the phenomena of magnetic ordering;
4. He will know the various aspects of the phenomenology of superconducting materials,
the microscopic mechanism of superconductivity and the formation of Cooper pairs;
5. He will be able to describe the behavior of Josephson junctions and SQUID devices,
with particular regard to quantum interference in the presence of a magnetic field;
6. He will know the basic principles of the linear interaction between electromagnetic
radiation and matter in terms of complex dielectric constant;
7. He will be able to interpret the experimental observations on the optical properties
of the condensed matter with simple classical and quantum models;
8. He will know how to describe the principles of radiation amplification and laser action
with rate equations models;
9. He will be able to characterize the properties of various types of lasers, continuous
or pulsed, and of the coherence of the emitted radiation;
Course syllabus and organization

Single session

Lesson period
First semester
The lectures can be delivered entirely remotely, according to the official calendar, in case of mobility restrictions due to the health emergency. In this case, the Zoom platform will be used with connection to a virtual classroom of the Physics Department, in synchronous connection and with real-time interaction between students and the teacher. In the lesson we will use a graphic tablet and the projection of slides. At the request of students it is possible to organize tutoring meetings in presence. The (oral) exams will always be carried out with the Zoom platform, in a virtual classroom or in a dedicated virtual meeting. Program and reference materials are not changed.
Course syllabus
1) Electronic properties of solids: insulators, metals and semiconductors. Crystals: diffraction and reciprocal lattice. Electrons in the periodic potential: band theory and Brillouin zones. Occupation of band states, Fermi surfaces. Electron dynamics and effective mass. Bloch oscillations.
2) Electronic bands in a magnetic field, Landau levels. De Haas-Van Alphen effect and experimental determination of Fermi surfaces.
3) Semiconductors: valence and conduction bands, hole concept, hints on doped semiconductors. Low dimensional structures.
4) Magnetic phenomena: Origin of magnetism in condensed matter. Paramagnetism and diamagnetism in molecules, insulators and metals, Curie's law. Magnetic ordering and ferromagnetism: exchange interaction and Heisenberg model. Ferromagnetic transition and critical exponents. Curie-Weiss law. Magnetic excitations: spin waves, magnons and their properties.
5) Superconductivity: phenomenology of the superconductive state, Meissner effect. Quantization of the magnetic field flux. Cooper pairs and elements of BCS theory. Analogies and differences with the superfluidity for bosons. Characteristic lengths. Junctions and tunnel effect: Josephson DC and AC effects. Junction in a magnetic field : quantum interference, SQUID devices and applications.
6) Elements of the theory on radiation-matter interaction: Maxwell's equations in condensed matter. Absorption, dispersion and complex dielectric tensor. Linear response and generalized susceptibility, Kramers-Kronig relations. Electric dipole interaction, classical and quantum microscopic models. Optical properties of insulating solids, metals and semiconductors. Excitons and other quasi-particles. Quantum well, quantum dots, photon confinement structures.
7) The laser and the generation of coherent radiation.
Spontaneous and stimulated emission, population inversion. Principles of laser action: amplification and feedback in the optical cavity, balance between gain and loss. 4-level laser scheme: rate equations, threshold, gain saturation. Homogeneous and inhomogeneous broadening of emission spectrum. Properties of various types of lasers. The laser as a dynamic dissipative system.
Prerequisites for admission
Fundamental concepts of: a) non relativistic quantum mechanics, in particular for applications to the harmonic oscillator, the potential well and the angular momentum, also with perturbative developments; b) classical and quantum statistics, partition functions and thermodynamic functions; c) Hamiltonian of interaction with the electromagnetic field and electric dipole approximation; d) oscillations of the crystal lattice and phonons.
Teaching methods
The teaching is provided in the classroom through lectures, discussions and slide shows. Attendance is strongly recommended.
Teaching Resources
The topics covered can be found largely in the lecture notes of the teacher, downloadable from the University's ARIEL educational website https://fcastellismca.ariel.ctu.unimi.it/v5/home
Moreover, here are some recommended books for completeness and further information:
1) S.M.Girvin and K.Yang, "Modern Condensed Matter Physics", Cambridge University Press 2019
2) M.L.Cohen and S.G.Louie, "Fundamentals of Condensed Matter Physics", Cambridge University Press
3) N.W.Ashcroft and M.D.Mermin, "Solid state Physics",
Saunders College, Philadelphia
Assessment methods and Criteria
The examination consists of an interview that focuses on the topics covered in the course. During the exam, lasting a minimum of 1 hour, both the skills and the critical abilities acquired by the student in the study of the phenomena treated will be evaluated, with particular regard to the essential use of quantum mechanics for their description. The result of the exam is expressed in thirtieths.
FIS/03 - PHYSICS OF MATTER - University credits: 6
Lessons: 42 hours
Professor: Castelli Fabrizio
tuesday 14:30 - 19:00
Department of Physics, via Celoria 16 Milan (fifth floor, room A/5/C3)