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 the quantity (called a “topological invariant”) finally changes.
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.
What is the focus of this course?
- Applications of topology in condensed matter based on bulk-edge correspondence.
- Special attention to the most active research topics in topological condensed matter: theory of topological insulators and Majorana fermions, topological classification of “grand ten” symmetry classes, and topological quantum computation
- Extensions of topology to further areas of condensed matter, such as photonic and mechanical systems, topological quantum walks, topology in fractionalized systems, driven or dissipative systems.
What tools does this course use?
- Simple thought experiments that rely on considerations of symmetry or continuity under adiabatic deformations
- Computer simulations similar to those used in actual research will give a more detailed and visual understanding of the involved concepts
- Dissecting research papers that teaches you to simply understand the idea even in the rather involved ones.
This course is a joint effort of Delft University of Technology, QuTech, NanoFront, University of Maryland, and Joint Quantum Institute.
- 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 topology, and critically understand it on your own.
- Acquire skills required to engage in research on your own, and to minimize confusion that often arises even among experienced researchers.
- 00. Before you begin
- 01. Topology in toy models
- 02. Majoranas I
- 03. More parameters: charge pumping
- 04. Chern insulators
- 05. Quantum spin Hall effect
- 06. Three-dimensional topological insulators
- 07. Topological defects
- 08. General approach to topological classification
- 09. Anderson localization and topology
- 10. Extensions of classification I
- 11. Extensions of classification II
- 12. Beyond single-particle physics