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Electronic Structure of Solids

Module PH2275

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Module version of WS 2018/9

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions
WS 2020/1WS 2019/20WS 2018/9

Basic Information

PH2275 is a semester module in German or English language at which is offered in winter semester.

This Module is included in the following catalogues within the study programs in physics.

  • Specific catalogue of special courses for condensed matter physics
  • Specific catalogue of special courses for Applied and Engineering Physics
  • Complementary catalogue of special courses for nuclear, particle, and astrophysics
  • Complementary catalogue of special courses for Biophysics

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

Total workloadContact hoursCredits (ECTS)
150 h 60 h 5 CP

Responsible coordinator of the module PH2275 in the version of WS 2018/9 was Christian Pfleiderer.

Content, Learning Outcome and Preconditions


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

Learning Outcome

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.

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VO 2 Electronic Structure of Solids Pfleiderer, C.
Assistants: Wilde, M.
Tue, 14:15–15:45, PH 2224
and singular or moved dates
UE 2 Exercise to Electronic Structure of Solids Wilde, M.
Responsible/Coordination: Pfleiderer, C.
Wed, 16:00–17:30, PH 2224

Learning and Teaching Methods

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)

Module Exam

Description of exams and course work

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?

Exam Repetition

The exam may be repeated at the end of the semester.

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