Theoretical Solid State Physics

I) Symmetries and structure of condensed matter

1. Phases and broken symmetries
2. Determination of structure by x-ray diffraction

II) Lattice vibrations

1. Phonons and thermodynamics
2. Neutron scattering, dynamic structure factor
3. Anharmonic effects, melting, Lindemann criterion

III) Electrons

1. Bonding types, stability
2. Bloch theorem, Wannier functions, band theory
3. Fermi surfaces, Thermodynamics
4. Semiclassical dynamics of electrons, Bloch oscillations
5. Edge state theory of the quantum Hall effect

IV) Many particle effects and disorder

1. Interacting electron gas, screening, Wigner lattice
2. Density Functional Theory
3. Electron-Phonon interaction, BCS-theory of superconductivity
4. Anderson localization in disordered quantum systems

Details on https://www.cmt.ph.tum.de/index.php?id=63

Successful participation provides the following skills:

1. Mathematical formulation of relevant structures of matter and their atomic composition. Calculation of the structural and dynamic properties of matter in terms of simple models

2. Explain the physics of structural phase transitions at surfaces and for defect structures

3. Understand modern methods for calculating the electronic structure of solids. Ability to perform simple density functional calculations

4. Approximations and methods for solving many particle problems in condensed matter physics

5. Understand and explain the nature of correlated low-dimensional systems in the framework of Fermi- or Luttinger liquid theory

6. Explain and theoretically describe electronic phase transitions such as superconductivity

No preconditions in addition to the requirements for the Master’s program in Physics.

The module consists of a lecture and exercise classes.

In the thematically structured lecture the learning topics is presented. With cross references between different topics the universal concepts in physics are shown. In scientific discussions the students are involved to stimulate their analytic-physics intellectual power.

In the exercise (ca. 6-8 students) the learning content is deepened and exercised using problem examples and calculations. Thus the students are able to explain and apply the learned physics knowledge independently.

e-learning (tablet PC with voice recording for listening to parts or whole lectures/exercises), presentation documents, exercise sheets, computer simulations, accompanying website, supplementary literature

• N.W. Ashcroft and N.D. Mermin, Solid State Physics, Cengage Learning (Deutsche Ausgabe: De Gruyter Oldenbourg)
• P.M. Chaikin and T.C. Lubensky, Principles of Condensed Matter Physics, Cambridge University Press

There will be a written exam of 90 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using calculation problems and comprehension questions.

For example an assignment in the exam might be:

• Calculate the spectrum of eigenfrequencies for the longitudinal vibrations of the two-atomic chain harmonic chain, assuming periodic boundary conditions.
• Determine the wave-function from the Bloch-condition for the Kronig-Penney model.
• Calculate the density correlation function of the non-interacting Fermi gas.
• Determine the relationship between fluctuations and dissipation.