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).

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.

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.

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.

[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.

Final exam: oral.

Requirement: completed 7 out of 11 problem sets.

Program and organizational details in a PDF format

• 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.