## Physics Seminar

### A contemporary view on topological band theory and new Euler class phenomena

**Speaker: Robert-Jan Slager (Cambridge University)**

**Date: Tuesday 1 March 2022**

**Time: 15:00**

**Venue: N/3.23**

In this talk, I will cover a selection of our recent work on topological characterizations in a rather colloquial style. In particular, I will review how constraints on symmetry eigenvalues can directly be linked to topological invariants, reproducing involved K-theory evaluations from a simple algorithmic point of view. The resulting conditions can then be extended to contemporary classification schemes by comparing to real space configurations, going by the name topological quantum chemistry or symmetry indicators.

The above developments, more importantly, indicate presence of topological phases beyond the above framework, an archetypal example being phases characterized by so-called Euler class. Hence, in the second part, I will discuss recent work on such systems, focussing on two new physical effects. Namely, I will first show that systems having non-trivial Euler class are intimately related to reciprocal conversion effects in materials that feature band nodes. Accordingly, I will motivate that Euler class Hamiltonians also pose new avenues in cold atomic gasses, inducing distinct quench dynamics, and other types of physical systems, notably phonon spectra as well as electron systems.

**Short bio:** Robert-Jan Slager obtained his PhD degree in Leiden University in 2016. Then, he worked as a postdoctoral researcher at Max Planck Institute for the Physics of Complex Systems until 2018 and at Harvard University until 2019. In 2019, he moved to Cambridge as a Principal Investigator and was awarded Marie-Curie individual fellowship and, Winton Group leader grant and Elected SPR fellow. He was awaded UKRI New Investigator grant in 2021 and ERC Starting grant this year.

**Personal webpage:** http://www.tcm.phy.cam.ac.uk/~rjs269/index.html