Casimir Course - Topology in Condensed Matter (to be taken anytime)







This is a open online course on topology in condensed matter. Initially developed for the edX platform in 2015, its development continues. Through this course we want to provide an introduction to the topic of topology in condensed matter. We want it to be accessible and useful to people with different backgrounds and motivations.

Course description
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.

Course structure: The course is separated into 12 topics, each containing 2–3 lectures on related subjects. Each lecture is introduced by an expert in this subject. We end each topic with suggestions of open-ended questions for self-study: numerical simulations or papers to read and review.

Course details

Dr. A. Akhmerov
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.
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 the TopoCondMat-website.
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 the TopoCondMat-website.
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.
Contact hours
3 hours per week; 8 weeks
Graduate School Credits
5 GSCs to PhD students who have successfully completed this course.

Please contact the responsible PI, Anton Akhmerov (, to register for this course.