Quantum Materials: Topological Matter

Course goals

The goal of the set of four courses in “Quantum Materials” is to provide the students with the necessary knowledge to master the electronic, magnetic, topological and superconducting properties of nanoscale quantum materials, both from a theoretical and experimental point of view.

Upon completion of the “Quantum Materials: Topological Matter” course, the students will have developed

1. an advanced understanding of the electronic properties of crystals and of the dynamics of electrons (free and in a crystal)
2. knowledge of the topological band theory and topological invariants, and the connection between topological properties and crystal symmetries
3. the ability to analyze, interpret, and critically evaluate contemporary research literature in the field of topological matter.

 

Content

All materials can be considered ‘quantum’ as their fundamental properties ultimately depend on their atomic structure, which is ruled by the laws of quantum mechanics. However, only a set of materials can show quantum properties at macroscopic length and time scales. The latter are called Quantum Materials, and include a wide range of materials such as Dirac materials (eg. Graphene), topological insulators and superconductors.
The course “Quantum Materials: Topological Matter” focuses on the study of theory and numerical simulations of topological materials, namely materials where the transport of information (electric charge) is protected by crystal symmetries. Notable experimental cases (eg. Hall effects) will also be discussed in the course.

The course “Quantum Materials: Topological Matter” builds on the master course “Fundamentals of Quantum Materials” (SK-MFUNQM; coordinator I. Swart) and should be complemented by the courses “Quantum Materials: Superconductors” (SK-MQUSU; coordinator Z. Zanolli, lecturers: I. Swart and Z. Zanolli) and “Magnetic Materials” (SK-MMAMA; coordinator M. Kamminga).

Tentative general program
The course is held part-time for 10 weeks, namely 4 hours per week (lectures and/or excercises)
Week 1: Review of previous knowledge: Electrons in crystals (Kaxiras Ch. 2)
Week 2: Magnetism and magnetic order (Lacroix, Blügel, Shankar Ch 14, 15)
Week 3:  Relativistic effects in atoms and solids
                   Time reversal symmetry and Inversion symmetry
Week 4: Quantum Transport from Zero to Hero, Graphene
Week 5: Topological Band Theory: Berry’s Phase, Polarization, Chern number, Bulk-Boundary Correspondence
                  Topology in 1D: The Su Schrieffer Heeger chain
Week 6: Topology in 2D: Integer Quantum Hall Effect, Haldane model of graphene
Week 7: ℤ2 topological insulators: Quantum Spin Hall effect, Kane-Mele model of graphene
Week 8: Topology in 3D (Kane ‘Topological Band Theory’ Ch 6)
Week 9: revision week
Week 10: exam (see MyTimetable for place and time)

Anonymous self-assessment before enrolling the course
This self-assessment tool is designed to help you gauge your readiness for the Quantum Materials: Topological Matter course. It will point to key concepts necessary for success in the course, allowing you to identify areas for review.  
https://forms.office.com/e/CLZsbn1Uxg