Speaker

Mr. Arthur Morris / Theory of Condensed Matter Group, University of Cambridge

Title

Non-Abelian Hopf-Euler insulators

Abstract

Many free-fermion topological phases of matter such as the Chern insulator are characterised by topological quantum numbers assigned to single isolated bands. While such single-band phases are now well understood, intriguing features remain to be explored within topological band theory. I will explain how nodes in real Bloch Hamiltonians carry non-Abelian topological charges which arise from the geometry of the classifying space. Moreover, by braiding these nodes around each other in reciprocal space, it is possible to induce a 'multi-band' topological phase, where the two band subspace supporting the nodes is labelled with an integer, the Euler class.  Another example of a multi-band topological invariant is the Hopf invariant, which characterises three dimensional complex phases and provides a solid state realisation of the Hopf fibration. Such systems can also host Chern numbers on each coordinate plane within the Brillouin zone; I will describe how the presence of such subdimensional invariants influences the bulk Hopf invariant. Finally, I will discuss a real topological phase in 3D which possesses a bulk Hopf invariant and 2D Euler classes. These systems have nontrivial quantum geometry, and appear to host unusual nodal line structures.

Biography

I completed my undergraduate and master’s in theoretical physics at the University of Oxford, graduating in 2021. I then moved to the Theory of Condensed Matter group in the University of Cambridge for my PhD, where I am supervised by Robert-Jan Slager. I am in Japan as a JSPS summer fellow, visiting the Oka group in the Institute of Solid State Physics, University of Tokyo.

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