## 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 become proficient in the analysis of a physical theory. The second objective is to learn how to distill the essentials from a set of advanced review and current research articles. The third 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 (20 minutes, with written handout) on a subject of their choice, and submit a report summarizing 3 publications chosen from a reading list.

The presentation can be done jointly with another student, the summaries are individual work.The final grade will be based on all three course aspects: the presentation, the summaries, and engagement in the tutorials.

## collected exercises

## Dates & Topics

Monday 6 February 9.00-11.00 overview no exercises — Snellius-4.12Monday 13 February 9.00-11.00 Dirac fermions in graphene: chiral symmetry, winding numberexercise 1 — Huygens-2.07Monday 20 February 9.00-11.00 Chiral symmetry in 1D: SSH chain, zero-modesexercise 2 — Snellius-4.12Monday 27 February 9.00-11.00 Chern insulator: Chern number, chiral edge states, quantum Hall effectexercise 3 — Huygens-2.07Monday 6 March 9.00-11.00 Quantum spin Hall effect: Kramers degeneracy, helical edge states, scattering matrixexercise 4 — Snellius-4.12Monday 13 March 9.00-11.00 Topological insulators: fermion doubling, half-integer quantum Hall effectexercise 5 — Huygens-2.07Monday 20 March 9.00-11.00 Topological superconductors: Kitaev chain, Majorana fermionsexercise 6 — Snellius-4.12Monday 27 March 9.00-11.00 Weyl semimetals: Berry flux, Fermi arcs, chiral magnetic effectexercise 7 — Huygens-2.07Monday 3 April 9.00-11.00 Symmetry classification: ten-fold way, topological invariantsexercise 8 — Snellius-4.12Monday 17 April 9.00-11.00 NO CLASSNO CLASSMonday 1 May 9.00-11.00 Topological quantum computation: Majorana qubits, braidingexercise 9 — Huygens-2.07Monday 8 May 9.00-11.00 Presentations (1) — Snellius-4.12Monday 15 May 9.00-11.00 Presentations (2) — Huygens-2.07