Applications for the class of 2020-2022 are still open for self-financed students. Apply here

Deadline : June 15th, 2020 (midnight, Paris time).  Applications for scholarships are closed. 


Covid-19 updates: during the Covid-19 pandemic, the SERP+ master is taking measures to ensure that learning can continue with new teaching and assessment methods.

Master SERP+ Programme

Introduction to Solid State


Content

The course gives an introduction to the basic properties of materials in the solid phase. Emphasis will be given to the properties for which a quantum mechanical treatment is mandatory. The course will cover the electronic band structure, the electronic excitations, the lattice dynamics as well as the magnetic properties of a crystal.

Theoretical part: frontal classes

Condensed Matter and Quantum mechanics

  • Failure of classical mechanics in the description of condensed matter.
  • Properties associated with the discreteness of matter: normal modes and phonons.
  • Concept of wavevector, its quantization in on the lattice and phonon density of states.
  • The heat capacity of a solid: Einstein and Debye models.
  • Chemical bonds, unit cell and symmetry properties.
  • Concept of direct and reciprocal space.
  • Probing the crystal lattice: scattering of electrons, neutrons and X rays off three and two-dimensional lattices.

The electronic and optical properties

  • Free electron gas in electric and magnetic fields.
  • Fermi Dirac statistics and the specific heat of an electron gas.
  • The Fermi energy, wavevector and surface of a solid.
  • The band structure and the single particle approximation for the valence electrons.
  • Dielectric response function, plasmon and surface plasmon.
  • Photoemission spectroscopy and work function.
  • The tight binding model: valence and conduction bands, metals, semiconductors and insulators. Electrons and holes , and their ffective mass.
  • Doping of semiconductor, semiconductor junctions and devices.

Magnetism

  • The various magnetic properties of a solid: para, dia, ferri and ferro-magnetism.
  • The magnetism of conduction electrons: Pauli paramagnetism and Landau diamagnetism.
  • Magnetic anisotropy, magnetic domains and hysteresis.
  • Understanding magnetism: Heisenberg Hamiltonian and Hubbard model for ferromagnetism.

Laboratory training:

  • Vibrational properties of a swinging string and resonance properties of diapasons.
  • The resonance conditions in electronic circuits.
  • Diffraction of light from a two dimensional lattice.
  • Low energy electron diffraction from a surface.
  • Measurement of the Hall effect.
  • Measurement of the threshold frequency in photoemission.

Aims

Achieving a thorough understanding of the properties of condensed matter at the microscopic level. Students will master the concepts of crystal lattice, lattice dynamics, electronic band structure, dielectric response and electronic excitations, magnetic properties and excitations, as well as the origin of metallic, semiconductor and insulator behavior.

Pre-requiste

Mathematics: Solution of linear and differential equations. Fourier analysis.

General Physics: Mechanics, Electromagnetism, Thermodynamics, and Waves.

Quantum Mechanics: quantum state and quantum numbers for a well and for an atom, Hamiltonian and Schroedinger equation, harmonic approximation, Heisenberg indetermination and Pauli exclusion principle, and perturbation theory.

Recommended Books

  • Steve, H. Simon: Lecture notes for Solid State Physics
  • Additional material will be provided by the lecturer.

Teaching Staff

Prof. Mario Rocca

Hours

Lectures: 40 hours
Laboratory: 20 hours

Grading System

Laboratory reports 20%
Final oral exam: 80%