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

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  • UserRobert-Jan Slager (University of Cambridge)
  • ClockThursday 11 November 2021, 13:15-14:30
  • HouseTheory Library.

If you have a question about this talk, please contact Dr Hannah Price.

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.

This talk is part of the Theoretical Physics Seminars series.

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