Electronic Structure of Solids

In this module, aspects of the electronic structure of crystals ranging from the basics to topics of current research are treated from the viewpoint of an experimental physicist. The interplay of experiment and theory relevant for both the determination and the understanding of electronic structures is explained using seminal examples. This creates a direct and sanguine access to the subject matter, without loosing oneself in "dry theory". The module has the following content:

• Basic concepts including electronic bonds, electronic bands and crystal symmetries.
• Techniques for band structure calculations: Starting from the simple quasi-free electron picture and the tight-binding description up to modern techniques for the calculation of realistic band structures including density functional theory.
• Experimental determination of Fermi surfaces and band structures using quantum oscillations. Further, Angular Correlation of Electron-Positron Annihilation Radition (ACAR) and Compton Scattering, as well as Angle-Resolved Photoemission Spectroscopy (ARPES)  are introduced.
• Influence of electron-electron interaction: Coulomb-Exchange interaction, quasiparticle concept und Fermi liquids, electronic instabilities.
• Influence of spin-orbit coupling
• Topological properties: Quantum-Hall effect, Chern number and Berry curvature. Topological insulators
• Unconventional fermion systems: Graphene, Weyl- and Dirac-half metals. "Heavy fermion" systems

After successful participation, the students are able to explain the basic concepts of the description of the electronic structure of crystalline condensed matter. This includes concepts of electronic bonds and electronic band structure. The students can discuss modern techniques for the calculation of realistic band structures. They can characterize methods for the experimental determination of Fermi surfaces and assess their capabilities. They can comment on influences of the electron-electron interaction and on consequences of the spin-orbit interaction. The students are in a position to discuss basic topological classifications of electronic structures.

In addition, the students are able to connect certain physical material properties to it´s electronic structure. They can describe seminal example systems for various important phenomena in current research.

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

This module consists of a lecture and an excercise course.

During the lecture the basics of both, theory and experimental methods are explained and elucidated by tangible examples. Digital handwriting is used to maintain an adequate pace while developing the basic principles. Functional relationships are illustrated using interactive graphics and short example programs. Open discussions with the students are an important integral part of the lecture. In the examples, experiment and theory are treated on an equal footing, highlighting their close integration.

During the excercises the knowledge is deepened by applying the learned concepts to selected examples. A hybrid approach is chosen where alongside the classical excercises, prefabricated interactive example programs are used and extended by the students in order to visualize relationships and examine the relevance of various parameters. Programming skills are not required.

Digital handwriting using Tablet-PC, lecture slides and dynamic graphics, example computer programs, lecture notes with literature references, excercises and examples

• J. Singleton: Band Theory and Electronic Properties of Solids, Oxford University Press, (2001)
• R.G. Chambers: Electrons in Metals and Semiconductors, Springer, (1990)
• D. Shoenberg: Magnetic Oscillations in Metals, Cambridge University Press, (2009)
• R.M. Martin: Electronic Structure: Basic Theory and Practival Methods, Cambridge University Press, (2008)

There will be an oral exam of 25 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using comprehension questions, sample calculations and discussions on the basis of sketches, diagrams and formulas.

For example an assignment in the exam might be:

• Which forms of electronic bonds exist in solid-state crystals?
• Which theoretical band structure calculation methods do you know and what are the major differences?
• State the Hamiltonian of a free electron in two dimensions in a magnetic field and sketch the solution of the time-independent Schrödinger equation.
• Describe the de Haas-van Alphen effect. Explain the benefit of the effect in determining Fermi surface properties.
• What is "unconventional" about the electronic properties of graphene?