Topological Quantum Matter


This literature provides background and context to the material covered in the course. It also contains much additional material.

Topics in Theoretical Physics is a student seminar course. The course is built around a current physics research topic. The topic for Spring 2023 is "Topological Quantum Matter". Subjects that will be discussed include: Topological insulators, quantum (spin) Hall effect, bulk-edge correspondence, chiral and helical edge modes (Dirac fermions), topological superconductors, Majorana fermions and vortex zero-modes, universality classes (tenfold way), topological invariants (Chern number), Weyl semimetals and surface Fermi arcs.

The purpose of the course is to become familiar with research methods. The first objective is to learn how to distill the essentials from a set of advanced review and current research articles. The second objective is to present this material comprehensibly both in a lecture form as well as in a written summary.

Lectures will provide background material and put the topic into a broader context. The topic is further developed in tutorials (instruction classes), where students will be asked to present their solutions to problems handed out in advance. Some of these problems may ask for computer programming.

At the end of the course, each student will give an oral presentation (with written handout) on a subject of their choice, and submit a report summarizing 3 publications chosen from a reading list. The final grade will be based on all three course aspects: the presentation, the report, and engagement in the tutorials.

collected exercises

 Dates & Topics

Monday 6 February

overview no exercises

Monday 13 February

Dirac fermions in graphene: chiral symmetry, winding number exercise 1

Monday 20 February

Chiral symmetry in 1D: SSH chain, zero-modes exercise 2

Monday 27 February

Chern insulator: Chern number, chiral edge states, quantum Hall effect exercise 3

Monday 6 March

Quantum spin Hall effect: Kramers degeneracy, helical edge states, scattering matrix exercise 4

Monday 13 March

Topological insulators: fermion doubling, half-integer quantum Hall effect exercise 5

Monday 20 March

Topological superconductors: Kitaev chain, Majorana fermions exercise 6

Monday 27 March

Weyl semimetals: Fermi arcs, chiral magnetic effect exercise 7

Monday 3 April

Random-matrix theory: ten-fold way, topological invariants exercise 8

Monday 17 April

topological quantum computation: Majorana qubits, non-Abelian braiding exercise 9

Monday 1 May

reserved for overflow

Monday 8 May

Presentations (1)

Monday 15 May

Presentations (2)