logo Priv.-Doz. Dr. Oleksandr Tsyplyatyev
About me
Research
Teaching
Publications

Theory of magnetism, superconductivity, and electronic correlations

Alex Tsyplyatyev, SS 2020

Lectures: 3 hours per week
Room: Online, including zoom on Wednesdays 10:15-11:00 
First week: 22.04.2020
Last week: 17.07.2020 (13 weeks of lectures in total)

Tutorials: 2 hours per week, 1 group
Tutorial organiser: Mr. Viktor Hahn/Mr. Dmytro Tarasevych
Tutor: Mr. Viktor Hahn/Mr. Dmytro Tarasevych
Room: Online, zoom on Fridays 10:15-12:00

This course is the second part of the introduction to the theory of condensed matter for all students starting from the 6th semester. It covers three main topics: Fermi liquid, superconductivity, and the basic principles of magnetism. The prerequisites for this course are Quantum Mechanics I (VTH4) and Thermodynamics and Statistical Physics (VTH5). The solid-state theory I is suggested but is not necessary, the major part of the course can be understood without it.

Announcements

Due to the coronavirus, and the ongoing lockdown, this course will be conducted online. To sign up  you need to send an email to tsyplyatyev[at]itp.uni-frankfurt.de with the following information: your name, surname, Matrikelnummer, and contact email. You will receive access to all materials, including zoom sessions.

If university life returns to normal before the end of this semester, we will switch back to the regular lecture and tutorial classes in the normal rooms and at the regular times.

You can find the organisational details for this course here. Read them carefully as they are not usual! Note that some details may change further due to the challenging circumstances, which we all are in this semester.

The tutorial classes start on Friday the 8th of May.

Lectures

  1. Week
  2. Week
  3. Week
  4. Week
  5. Week
  6. Week
  7. Week
  8. Week
  9. Week
  10. Week
  11. Week
  12. Week
  13. Week
Complete lecture notes

Problem sheets

  1. Normalisation of N-body wavefunctions, projection operators, fermionic annihilation operator (Hahn)
  2. Conservation of the particle number, Matrix representation of fermionic operators, Two site Hubbard model (Tarasevych)
  3. Hartree-Fock effective mass, screened Coulomb interaction, quasiparticle energy at finite temperature (Hahn)
  4. Density response of free electrons, Limits of density response (Tarasevych)
  5. Current density operator, Equations of motion of the Ginzburg-Landau theory, Coherence length of a superconductor (Hahn)
  6. Josephson effect, Ferromagnetic and superconducting sphere (Tarasevych)
  7. Mean size of a Cooper pair, Canonical transformation of the Fröhlich Hamiltonian (Hahn)
  8. Creation and annihilation operators of Cooper pairs, Bogoliubov transformation for fermions and bosons, Anderson's pseudo-spin formulation (Tarasevych)
  9. BCS density of states, Fluctuations of the number of particles in the BCS ground state, Specific heat of a BCS superconductor (Hahn)
  10. Landé g-factor, Electrons in a uniform magnetic field (Tarasevych)
  11. Spin representations, Linear chain of three spin-half particles, Diagonal elements of a product of spin operators (Hahn)

Master solutions

  1. Normalisation of N-body wavefunctions, projection operators, fermionic annihilation operator (Hahn)
  2. Conservation of the particle number, Matrix representation of fermionic operators, Two site Hubbard model (Tarasevych)
  3. Hartree-Fock effective mass, screened Coulomb interaction, quasiparticle energy at finite temperature (Hahn)
  4. Density response of free electrons, Limits of density response (Tarasevych)
  5. Current density operator, Equations of motion of the Ginzburg-Landau theory, Coherence length of a superconductor (Hahn)
  6. Josephson effect, Ferromagnetic and superconducting sphere (Tarasevych)
  7. Mean size of a Cooper pair, Canonical transformation of the Fröhlich Hamiltonian (Hahn)
  8. Creation and annihilation operators of Cooper pairs, Bogoliubov transformation for fermions and bosons, Anderson's pseudo-spin formulation (Tarasevych)
  9. BCS density of states, Fluctuations of the number of particles in the BCS ground state, Specific heat of a BCS superconductor (Hahn)
  10. Landé g-factor, Electrons in a uniform magnetic field (Tarasevych)
  11. Spin representations, Linear chain of three spin-half particles, Diagonal elements of a product of spin operators (Hahn)

Content of the course
  1. Second quantisation
  2. Fermi liquid
  3. Linear response
  4. Superconductivity
  5. Basic principles of magnetism
Literature
  • N. W. Ashcroft and N. D. Mermin, Solid State Physics, Sounders College Publishing, 1976. (main book)
  • D. J. Thouless, The Quantum Mechanics of Many-Body Systems, Dover Publishing, 2014.
  • M. Tinkham, Introduction to Superconductivity, Dover Publishing, 2004.
  • D. C. Mattis, The Theory of Magnetism Made Simple, World Scientific, 2006.