Theoretische Festkörperphysik
Theoretical Condensed Matter Physics

The aim of this module is to learn established and modern concepts in condensed matter physics. The module starts with the question what condensed matter physics is. After a brief recapitulation of crystal structures and classification, the module addresses X-ray elastic scattering and neutron inelastic scattering, with special emphasis on the analysis of the static and dynamic structure factors and the single mode approximation in the context of the Bijl-Feynman formula. Next are phonons, followed by tight-binding models including the dispersion of graphene and polyacetylene, but also highlighting the consequences of inversion symmetry, time reversal symmetry, and spin-obit coupling. Next is a phenomenological discussion on semiconductors. The second half of the module is devoted to the integer quantum Hall effect, the Berry phase and the role of topology, topological insulators and the fractional quantum Hall effect.  We finish the module by discussing Anderson localization and magnetism. The module does not use techniques from field theory.

After successful completion of the module the students are able to:

1. lUnderstand X-ray and neutron scattering
2. Understand the role of symmetry and topology in band structures
3. Compute phonon and tight-binding spectra
4. Explain the working of semiconductors
5. Compute the Berry phase
6. Understand the bulk-edge correspondence in topological materials
7. Work with Laughlin wavefunctions and composite fermions
8. Work through advanced condensed matter physics topics on their own

No prerequisites in addition to the requirements for the Master’s program in Quantum Science and Technology. Familiarity with quantum mechanics is assumed, at the level of an introductory module from a Bachelor degree in physics.

The module consists of a lecture series (4 SWS) and exercise classes (2 SWS), comprising one lecture sessions and one exercise session per week.

The main teaching material is presented on the blackboard or by beamer. Lectures are supplemented by weekly problem sets, deepening the understanding of core concepts through concrete calculations. Solutions to the problem sets are discussed in the exercise sessions.

Participation in the exercise classes is strongly recommended, since the exercises are aids for acquiring a deeper understanding of the core tools of condensed matter many-body physics and field theory and for practicing to solve typical exam problems.

Power point and Keynote presentations, blackboard or equivalent.

Standard textbooks on condensed matter physics, e.g.:

• Girvin and Yang, Modern Condensed Matter Physics
• Gross and Marx, Festkörperphysik
• Ashcroft and Mermin, Solid State Physics

There will be a written exam of 180 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using conceptual questions and computational tasks.

For example an assignment in the exam might be:

• What can be measured with neutron scattering?
• How do Dirac fermions arise in the dispersion of graphene?
• What is a Kramers doublet?
• What are the lowest type of excitations in the Su-Schrieffer-Heeger model?