Advanced Topics in Condensed Matter Physics

Course FSI3215 (7.5hp)

Instructors: Alexander Balatsky, Edwin Langmann, Konstantin Zarembo

Course Description

The course is aimed at introducing a number of topics in Condensed Matter Theory through the formalism of Green's functions. Topics will include:

  1. Green's functions
  2. Linear response theory
  3. Electron-phonon interactions
  4. Elements of Fermi liquid theory
  5. Green's functions at finite temperature
  6. Electrons in random potential
  7. Superconductivity
The course is based on a set of problems taken from the book L. S. Levitov and A. V. Shytov, "Green's functions. Theory and practice" .

Solutions to selected problems:

Problem 1
Green's Functions
Problem 2
Kubo formula
Problem 3
Electron-phonon interactions: electron self-energy
Problem 4
Phonon polarization operator
Problem 7
Matsubara technique
Problem 8
Scattering on impurities
Problem 11
Problem 12
Heat capacity of a superconductor
Problem 13
Symmetries of superconducting order: Solution 1; Solution 2

Prerequisites for the course are the working knowledge of quantum mechanics and familiarity with the basic concepts of condensed matter theory.

Ideally, this should be a reading course, where all the problems are solved in class. So pick a problem of your like and prepare to give a presentation on its solution along with an introduction to the underlying theory. You are encouraged nevertheless to solve all other problems on your own.

The course will include a guest lecture by Dmitri Khveschenko (University of North Carolina) on the disorder and interaction effects in graphene and other Dirac/Weyl metals.

Further information about the course can be found at KTH course directory


Session 1
Wednesday, March 25, 13:15-15:00 (FB41)
Session 2
Wednesday, April 1, 13:15-15:00 (FD41)
Session 3
Wednesday, April 15, 13:15-15:00 (FB41)
Session 4
Wednesday, April 22, 13:15-15:00 (FB41)
Session 5
Wednesday, April 29, 13:15-15:00 (FD41)
Session 6
Wednesday, May 6, 13:15-15:00 (FB41)
Session 7
Wednesday, May 13, 13:15-15:00 (FA31)
Guest lecture
Friday, May 15, 13:15-15:00 (FB54)

Dmitri Khveschenko, Scotch tape-induced relativity in graphene: Dirac fermions, chiral symmetry breaking, magnetic catalysis, (anti)localization, and all that.

In this short, yet comprehensive, review, we discuss the main effects of a pseudo-relativistic dispersion on the kinematics, localization properties and interaction-related instabilities in such Dirac (semi)metals as graphene and its analogues. The presentation does not require a prior exposure to the subject, other than the basic knowledge of quantum mechanics and many-body physics.

Session 8
Wednesday, May 20, 15:15-17:00 (FB41)
Session 9
Wednesday, June 3, 14:15-16:00 (FD41)