Condensed Matter Theory (PHY411)
Lecturer: Dmitri Ivanov
Course schedule:
- Lectures: Thu 10:15 - 12:00, room Y36-K-08 (from 21.02 until 30.05)
- Exercises: Wed 12:15 - 13:00, room Y36-J-81 (from 27.02 until 29.05)
- Exam: Tue Jun 25, 14:00 room HIT H 51 (ETH Hönggerberg). Exam rules (link).
- Exam topics: (pdf file). Complete lecture notes: (pdf file).
- Exercises: Wed 12:15 - 13:00, room Y36-J-81 (from 27.02 until 29.05)
Course program:
- 1. Introduction
- 1.1 Electrons in metals: methods and approximations.
- 1.2 Non-interacting fermions: specific heat, electrical and thermal conductivities, Wiedemann-Franz law.
- 2. Symmetries of electronic states in crystals.
- 2.1 Groups and their representations.
- 2.2 Crystal symmetries and degeneracies of energy bands.
- 3. Electron-electron interactions.
- 3.1 Second quantization, introduction to diagrammatic methods.
- 3.2 Hartree-Fock approximation.
- 3.3 Random-phase approximation and screening of Coulomb interactions.
- 3.4 Landau Fermi liquid theory.
- 3.5* Numerical approaches: density functional theory, local density approximation.
- 3.2 Hartree-Fock approximation.
- 4. Phonons and electron-phonon interactions.
- 4.1 Phonons. Specific heat of phonons.
- 4.2* Resistivity due to phonons.
- 4.3 Attraction between electrons mediated by phonons.
- 4.2* Resistivity due to phonons.
- 5. BCS theory of superconductivity.
- 5.1 BCS Hamiltonian and mean-field approximation.
- 5.2 BCS ground state, Cooper pairs, quasiparticles.
- 5.3 Relation between the transition temperature and the zero-temperature gap.
- 5.2 BCS ground state, Cooper pairs, quasiparticles.
- 1.1 Electrons in metals: methods and approximations.
Recommended books:
- [AM] N.W.Ashcroft and N.D.Mermin, Solid State Physics.
- [Mar] M.P.Marder, Condensed Matter Physics.
- [PC] P. Coleman, Introduction to Many Body Physics.
- [Mar] M.P.Marder, Condensed Matter Physics.
Course organization:
- Final exam: oral.
- Requirement: completed 7 out of 11 problem sets.
- Program and organizational details in a PDF format
- Requirement: completed 7 out of 11 problem sets.
Previous and forthcoming lectures:
- 21.02.13: Electrons in metals: methods and approximations (overview of the course). Specific heat and conductivity in the model of noninteracting fermions (Wiedemann-Franz law). Lecture notes and problem set (pdf).
- 28.02.13: Electronic band structure and lattice symmetries. Groups and their representations. Lecture notes and problem set (pdf).
- 07.03.13: Band structure and lattice symmetries: example of diamond. Lecture notes and problem set (pdf).
- 14.03.13: Interacting electrons: introduction to many-body methods. Second quantization and Wick theorem. Lecture notes and problem set (pdf).
- 21.03.13: Applications of the Wick theorem: density correlations in a free fermion gas and perturbative Hartree-Fock energy. Lecture notes and problem set (pdf).
- 28.03.13: Green's functions in quantum mechanics. Friedel oscillations of the density of states around an impurity. Lecture notes and problem set (pdf) .
- 11.04.13: Green's functions in many-body systems. Hartree-Fock approximation in the diagrammatic formulation. RKKY interaction. Lecture notes and problem set (pdf)
- 18.04.13: Screening of Coulomb interaction in a metal. Thomas-Fermi and Lindhard approximations. Lecture notes and problem set (pdf).
- 25.04.13: Fermi-liquid theory. Lecture notes and problem set (pdf).
- 02.05.13: Phonons. Electron-phonon interaction. Attraction between electrons mediated by phonons. Lecture notes and problem set (pdf).
- 16.05.13: BCS theory of superconductivity. Bogoliubov quasiparticles and the BCS ground state. Lecture notes and problem set (pdf).
- 23.05.13: BCS theory of superconductivity. Self-consistency equation for the gap and the critical temperature. Lecture notes (pdf).
- 30.05.13: Overview of the course.