Course schedule:

Lectures: Thu 09:15 - 11:00, room Y36-K-08 (from 19.02 until 28.05)

Exercises: Thu 11:15 - 12:00, room Y36-K-08 (from 26.02 until 28.05)

Complete lecture notes: (pdf file)

Exam: Wed Jun 24 13:30, room HIT E 41.1 (ETH Hönggerberg)

Exam rules and topics

Q&A session: Thu Jun 18 16:00, room HIT E 41.1 (ETH Hönggerberg)

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.

4. Phonons and electron-phonon interactions.

4.1 Phonons. Specific heat of phonons.

4.2 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.

Course organization:

Final exam: oral.

Requirement: completed 7 out of 10 problem sets.

Program and organizational details in a PDF format

• 19.02.15: 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).
• 26.02.15: Electronic band structure and lattice symmetries. Groups and their representations. Lecture notes and problem set (pdf).
• 05.03.15: Band structure and lattice symmetries: example of diamond. Lecture notes and problem set (pdf).
• 12.03.15: Band structure and lattice symmetries: example of diamond (continued). Interacting electrons: introduction to many-body methods. Second quantization. Lecture notes and problem set (pdf).
• 19.03.15: Second quantization (continued). Diagonalization of quadratic Hamiltonians.
• 26.03.15: Wick theorem and its applications. Density correlations in a free fermion gas and perturbative Hartree-Fock energy. Lecture notes and problem set (pdf).
• 02.04.15: Green's functions in quantum mechanics. Friedel oscillations of the density of states around an impurity. Lecture notes and problem sets (pdf) .
• 16.04.15: Green's functions in many-body systems. Hartree-Fock approximation in the diagrammatic formulation. Lecture notes and problem sets (pdf) .
• 23.04.15: Hartree-Fock approximation in the diagrammatic formulation (continued). RKKY interaction.
• 30.04.15: Screening of Coulomb interaction in a metal. Thomas-Fermi and Lindhard approximations. Lecture notes and problem set (pdf).
• 07.05.15: Phonons. Electron-phonon interaction. Lecture notes and problem set (pdf).
• 21.05.15: Electron-phonon interaction (continued). Attraction between electrons mediated by phonons. BCS theory of superconductivity. Bogoliubov quasiparticles and the BCS ground state. Lecture notes and problem set (pdf).
• 28.05.15: BCS theory of superconductivity (continued). Self-consistency equation for the gap and the critical temperature.