Theory of magnetism, superconductivity, and electronic correlationsAlex Tsyplyatyev, SS 2020Lectures: 3 hours per week Room: Online, including zoom on Wednesdays 10:1511:00 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 10:1512:00 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 solidstate theory I is suggested but is not necessary, the major part of the course can be understood without it. AnnouncementsDue 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.unifrankfurt.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 Week
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Complete lecture notesProblem sheets Normalisation of Nbody wavefunctions, projection operators, fermionic annihilation operator (Hahn)
 Conservation of the particle number, Matrix representation of fermionic operators, Two site Hubbard model (Tarasevych)
 HartreeFock effective mass, screened Coulomb interaction, quasiparticle energy at finite temperature (Hahn)
 Density response of free electrons, Limits of density response (Tarasevych)
 Current density operator, Equations of motion of the GinzburgLandau theory, Coherence length of a superconductor (Hahn)
 Josephson effect, Ferromagnetic and superconducting sphere (Tarasevych)
 Mean size of a Cooper pair, Canonical transformation of the Fröhlich Hamiltonian (Hahn)
 Creation and annihilation operators of Cooper pairs, Bogoliubov transformation for fermions and bosons, Anderson's pseudospin formulation (Tarasevych)
 BCS density of states, Fluctuations of the number of particles in the BCS ground state, Specific heat of a BCS superconductor (Hahn)
 Landé gfactor, Electrons in a uniform magnetic field (Tarasevych)
 Spin representations, Linear chain of three spinhalf particles, Diagonal elements of a product of spin operators (Hahn)
Master solutions Normalisation of Nbody wavefunctions, projection operators, fermionic annihilation operator (Hahn)
 Conservation of the particle number, Matrix representation of fermionic operators, Two site Hubbard model (Tarasevych)
 HartreeFock effective mass, screened Coulomb interaction, quasiparticle energy at finite temperature (Hahn)
 Density response of free electrons, Limits of density response (Tarasevych)
 Current density operator, Equations of motion of the GinzburgLandau theory, Coherence length of a superconductor (Hahn)
 Josephson effect, Ferromagnetic and superconducting sphere (Tarasevych)
 Mean size of a Cooper pair, Canonical transformation of the Fröhlich Hamiltonian (Hahn)
 Creation and annihilation operators of Cooper pairs, Bogoliubov transformation for fermions and bosons, Anderson's pseudospin formulation (Tarasevych)
 BCS density of states, Fluctuations of the number of particles in the BCS ground state, Specific heat of a BCS superconductor (Hahn)
 Landé gfactor, Electrons in a uniform magnetic field (Tarasevych)
 Spin representations, Linear chain of three spinhalf particles, Diagonal elements of a product of spin operators (Hahn)
Content of the course  Second quantisation
 Fermi liquid
 Linear response
 Superconductivity
 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 ManyBody Systems, Dover Publishing, 2014.
 M. Tinkham, Introduction to Superconductivity, Dover Publishing, 2004.
 D. C. Mattis, The Theory of Magnetism Made Simple, World Scientific, 2006.
