Course FSI3215 (7.5hp)

Instructors: Alexander Balatsky, Edwin Langmann, Konstantin Zarembo

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

- Green's functions
- Linear response theory
- Electron-phonon interactions
- Elements of Fermi liquid theory
- Green's functions at finite temperature
- Electrons in random potential
- Superconductivity

- 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
- Superconductivity
- 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)