The course aims at providing insights into the simple use of symmetry concepts to understand phenomena and material properties without performing detailed calculations. On the same basis, it gives some guides how to make minimal plans for experiments using the symmetry of the studied materials or vice versa how to determine the symmetry of materials from the output of experiments.

Performance record

oral exam

Online/Digitale Veranstaltung

Veranstaltung wird online/digital abgehalten.

Hauptunterrichtssprache

englisch

Miscellanea

The exercises will be uploaded. The discussion of the problems will take place via skype.

Contents: The topical outline of the course is as follows:
• Introduction and common examples
o Motivating examples
o Polar and axial vectors and tensors
o Spatial and temporal symmetries and charge conjugation
o Symmetries of measurable quantities and fields
o Symmetries of physical laws (classical and quantum)
o Conservation laws (linear and angular momentum, energy, etc.)
o Symmetry of measurement configurations (reciprocity, etc.)
• Neumann principle
o Linear response theory and Onsager relations
o Applications to vector and tensor quantities: electric and magnetic dipole moment of molecules; ferroelectricity, ferromagnetism, piezoelectricity and magnetoelectricity in crystals; wave propagation in anisotropic media (sound and light)
• Symmetry allowed energy terms
o On the level of classical free energy: Polar, nematic and magnetic order parameters (Landau expansion)
o On the level of Hamiltonians: Molecular vibrations, crystal field potential, magnetic interactions
• Symmetry of physical states
o Spatial inversion and parity eigenstates
o Discrete translations and the Bloch states
• Spontaneous symmetry breaking upon phase transitions (Landau theory)
• Outlook: Symmetry guides for skyrmion-host materials, multiferroic compounds and axion insulators