Multi-gap Euler topology in materials

Multi-gap Euler topology has recently emerged as new direction in the study of topological matter. In these systems, the energy spectrum is divided into three or more groups of bands, and C2T or PT symmetries enforce real Hamiltonians. The resulting system can be characterised using the Euler class, and these phases host exotic phenomena such as bulk band nodes carrying non-Abelian charges. Despite growing interest, the experimental observation of multi-gap topology in real materials is still missing. In this talk, I will propose several materials exhibiting multi-gap topology, with examples in both the electronic and phonon sectors. In particular, I will highlight that phonons could be an ideal platform for the exploration of multi-gap topology in real materials, and discuss associated experimental signatures for their observation.