Casimir Course - Topology in Condensed Matter





Education Period
None (Self Study)
Expected prior knowledge Absolute minimum: general knowledge of solid state physics and quantum mechanics, especially familiarity with band structures and the tight binding model.

Following Advanced Solid State Physics, Quantum Transport, and learning Python is recommended in parallel, or before the course.
Course Contents The idea behind topological systems is simple: if there exists a quantity, which cannot change in an insulating system where all the particles are localized, then the system must become conducting and obtain propagating particles, when this quantity (called "topological invariant") finally changes.

Frequently, the edges of such topological materials have properties that are impossible to achieve otherwise owing to the so-called "bulk-edge correspondence". It guarantees the existence of protected states at the edge and their robustness against anything that happens at the boundary.

The practical applications of this principle are quite profound, and already within the last eight years they have lead to prediction and discovery of a vast range of new materials with exotic properties that were considered to be impossible before.

Our central focus will be these very exciting developments with special attention to the most active research topics in topological condensed matter: namely the theory of topological insulators and superconductors following from the 'grand ten symmetry classes' as well as topological quantum computation and Majoranas.

We will complete this general picture with a discussion of some of the other ramifications of topology in various areas of condensed matter such as photonic and mechanical systems, topological quantum walks, topology in fractionalized systems, driven or dissipative systems.
Study Goals Learn about the variety of subtopics in topological materials, their relation to each other and to the general principles.

Learn to follow active research on topological effects in condensed matter, and critically understand it on your own.

Acquire skills required to engage in research on your own, and minimize confusion that often arises even among experienced researchers.
Education Method Most of the course is self-study, based on the online materials available at

In order to begin the course, try to coordinate your study with somebody else so that you can also discuss among each other—this is very helpful in a self-study course.

After an initial preparation of a topic, schedule a discussion with the course team via email or online via chat

During a discussion you will receive an assignment, which will be either a paper review or a numerical simulation, depending on your preferences.
Literature and Study Materials All the required materials are available online at
Assessment The course grade is fully based on the completion of assignments (60%) and participation in the discussions (40%).

For a successful completion you need to finish assignments for the first 7 weeks of the course, and 1 for one of the last 5 weeks.
Credits5 Graduate School credits will be awarded to the PhD students who have successfully completed this course.
RegistrationPlease contact the responsible PI, Anton Akhmerov: