Casimir Course - Topology in Condensed Matter (regular course and MOOC!)



10:45-12:45 hrs


Delft University of Technology, Applied Sciences, Lorentzweg 1, Delft (TN classroom 2, F206)


Responsible Instructor
Name E-mail
Dr. A.R. Akhmerov
Course dates and location
Every Monday from 13 February to 29 May (except 17 April), 10:45-12:45, room F206
Expected prior knowledge General knowledge of condensed matter theory and quantum mechanics on at least an advanced bachelor level.
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 The course will be tightly coupled with an online course provided by DELFTx (

The necessary information will be provided online. Based on this you will preform simple computer simulations of different topological phenomena, and relate important research papers to the materials that you learned.

The classes are not going to repeat the online materials. Instead we will clarify the questions (if there are any), discuss the results of your simulations and the reviews of the papers.
Reading All the required materials will be available online here.
Assessment The course grade is fully based on the completion of assignments (60%) and participation in the discussions (40%).

For a successful completion you are expected to perform most of the homework computer simulations, assess and summarize several papers, and describe/present your work in class several times.
Credits5 Graduate School credits will be awarded to the PhD students who have successfully completed this course.
This course has already started. To sign up for the MOOC, please use this link.