• View
• Edit
• History
• Print

CondensedMatter

Index

Prerequisites

This course must be contained in 6 ETS credits, i.e. 48 hours of front activities plus 72 hours of homework and study. It is formally optional, strongly recommended to Condensed matter students

In Parma this course comes after three undergraduate compulsory courses:

• 6 ETS credit covering classical statistical mechanics
• 9 ETS credit introduction to quantum mechanics that covers atoms
  • He atom
  • spin-orbit
  • many electron atoms, alcaline
  • Zeeman effect
• 6 ETS credit that cover molecules and solids, with suggested readings from Huang - Statistical Mechanics, Yeomans - Statistical Mechanics of Phase Transitions, Bruus and Flensberg - Introduction to Quantum field theory in condensed matter physics
  • Born Oppenheimer approximation
  • biatomic molecules: nuclear vibrations and rotationse rotazioni nucleari; hydrogen moelcule and molecular ion, bond and antibond
  • atomic molecules, hybridization
  • molecular spectroscopy: rotational, vibrational IR spectra, Raman
  • lattice and structures, symmetriy and Bravais, reciprocal lattice and diffraction
  • Lattice defects
  • lattice vibrations, dispersion for monatomic and biatomic chain, phonons
  • Thermal properties of solids, Einstain and Debye model
  • free electron model
  • Bloch states: energy bands, metals and insulators
  • Semiconductors and superconductors, basic properties
  • Magnetic properties: diamagnetism, Langevin and Pauli paramagnetism, ferromagnetic and antiferromagnetic order

The Master condensed matter syllabus includes the following compulsory courses

• 6 ETCS credits on advanced quantum mechanics
• 6 ETCS credit covering quantum statistical mechanics specific parts plus the following additional topics of interest
  • Density operator, statistical entropy
  • Einstein model for specific heat of solids,
  • examples of transport and diffusion phenomena
  • Susceptibility and fluctuations: static linear response
  • Fermi-Dirac and Bose-Einstein distributions
  • Phase transitions, order parameters, fluctuation divergence, Landau model, critical exponents, order-disorder transition in solid solutions, Ising model in 1D, Spin 1D Ising, Potts, Heisenberg and XY models, mean field approximation,
  • Fock space, creation and annihilation operators, Hubbard model, harmonic oscillator, boson spin representation, ferromagnets in Holstein-Primakoff approximation Fermi gas in Hartree-Fock

Top

Syllabus

• Recap of basic concepts done elsewhere: Born-Oppenhemer, the crystal structure and Bloch theorem, linear response, tight binding, lattice vibrations and phonons. This recap will focus on a few topics to introduce useful instruments, such as lattice visualization and how to use the Crystallografic Bilbao Server.
• The jellium model for the metal as a gymn: recap of Sommerfeld model, Hartree-Fock, exchange and the jellium corrections, the dielectric function.
• DFT: the basic to be able to run two examples, Si and Fe.
• Metal insulator transitions.
• Superconductivity.

Top

Textbooks

• Steven H. Simons The Oxford Solid State Basics, Oxford Univ. Press, 2013, a good bachelor level textbook, good mixture of phenomenology description and theory without too much formalism. Also video lectures available. Recommended reference for some prerequisite ideas and for other topics not treated here.
• Paul W. Anderson, Basic Notions of Condensed Matter Physics Benjamin/Cummings Press 1984, a text for further readings from a Nobel Prize winner who launched many of the leading notions on the field, certainly not the place to start
• Richard M. Martin Electronic structure. Basic theory and practical methods, Cambridge Univ. Press 2004, a good graduate level book for those condensed matter theory students. The early chapter are a good modern account of the fundamentals. Cambridge style, with details.
• James F. Annet Superconductivity, Superfluidity and Condensates, Oxford Univ. Press (Master Series), 2004 good balance between formalism and introduction, Superconductivity follow this book.
• Neil Ashcroft, David Mermin Solid State
  • Ch. 1 Bose Einstein condensation
  • Ch. 2 Superfluid Helium
  • Ch. 3 Superconductivity, phenomenology and London model
  • Ch. 4 Ginzburg- Landau
  • Ch. 5 Macroscopic coherence
  • Ch. 6 BCS
• Ulrich Rössler Solid State Theory: An Introduction, Physica-Verlag, here a selection of useful chapters
  • Ch. 2 Linear-response, Born-Oppenheimer
  • Ch. 3 Lattice vibrations classical and quantum
  • Ch. 4 Jellium, Fock space and Fermi surface, dielectric screening
  • Ch. 5 DFT
  • Ch. 7 Electronic correlations