Modelling topological phases of matter (Prof. Dr. Ralf Meyer)

Welcome to the reading class on modelling topological phases of matter. I offered this course in the winter term 2018–19 and recorded it for the benefit of a few students who could not attend in person. I prepared lecture notes for this course. Together with the recorded classes, this should make this material quite suitable for self-study. The course is intended for mathematics students and starts with a crash course on the quantum physics background. The mathematical tools that I use are comparatively basic. In particular, you need not know about C*-algebras and their K-theory. I use the language of homotopy theory instead to formulate the classification.

Links to recorded lectures

Date Topic and Recording Link
17.10.2018 Introduction Physics crash course I
24.10.2018 Physics crash course: rotations, projective representations, anti-unitary symmetries
7.11.2018No recording available
24.11.2018 Band theory: Spectrum of a Schrödinger operator with bounded periodic potential
21.11.2018 continuity of eigenvectors and eigenfunctions in band theory tight binding models graphene (begun)
28.11.2018 The graphene model
5.12.2018 The models by Semenoff, Haldane, Bernevig–Hughes–Zhang, and Su–Schrieffer–Heeger
12.12.2018 Homotopy of invertible Hamiltonians
19.12.2018 A crash course in homotopy theory
9.1.2019 Some basic homotopy theory
16.1.2019 More basic homotopy theory
23.1.2019 Homotopy classification for Hamiltonians with symmetries
30.1.2019 Bulk-edge correspondence in one dimension index and winding number