## Literature

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

- A short course on topological insulators by J.K. Asbóth, L. Oroszlány, and A. Pályi.
- An introduction to topological insulators by M. Fruchart and D. Carpentier.
- Introduction to topological phases in condensed matter by A.G. Grushin.
Topological Phases of Matterby R. Moessner and J.E. Moore (Cambridge University Press, 2021). No need to purchase this: it is available as an e-book free of charge for Leiden University students at the publisher.

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 9.00-11.00 overview no exercises Monday 13 February 9.00-11.00 Dirac fermions in graphene: chiral symmetry, winding numberexercise 1 Monday 20 February 9.00-11.00 Chiral symmetry in 1D: SSH chain, zero-modesexercise 2 Monday 27 February 9.00-11.00 Chern insulator: Chern number, chiral edge states, quantum Hall effectexercise 3 Monday 6 March 9.00-11.00 Quantum spin Hall effect: Kramers degeneracy, helical edge states, scattering matrixexercise 4 Monday 13 March 9.00-11.00 Topological insulators: fermion doubling, half-integer quantum Hall effectexercise 5 Monday 20 March 9.00-11.00 Topological superconductors: Kitaev chain, Majorana fermionsexercise 6 Monday 27 March 9.00-11.00 Weyl semimetals: Fermi arcs, chiral magnetic effectexercise 7 Monday 3 April 9.00-11.00 Random-matrix theory: ten-fold way, topological invariantsexercise 8 Monday 17 April 9.00-11.00 topological quantum computation: Majorana qubits, non-Abelian braidingexercise 9 Monday 1 May 9.00-11.00 reserved for overflow Monday 8 May 9.00-11.00 Presentations (1) Monday 15 May 9.00-11.00 Presentations (2)