CMT Forum: Titus Neupert

31 Jan 2024
Seminars and colloquia
Simpkins Lee

Titus Neupert (University of Zurich)

Seminar series
CMT Forum
Knowledge of physics?
Yes, knowledge of physics required
For more information contact

Topological Physics in Hyperbolic Lattices

Hyperbolic lattices tile the negatively curved hyperbolic plane. They recently emerged as a new paradigm of synthetic matter. A particularly appealing feature is that their energy levels are characterized by a band structure in a four-dimensional momentum space, even though the hyperbolic space is two-dimensional. I will give an overview over several results on hyperbolic lattices, including: (i) an experimental realization of a hyperbolic lattice using electrical circuits, (ii) an attempt to explore the topological aspects arising in hyperbolic band theory, by defining the hyperbolic Haldane model and the hyperbolic Kane-Mele model, (iii) a failed attempt to define four-dimensional topological states on a hyperbolic plane. The latter resulted in something way more interesting than the expected result: instead of a topological band insulator, we obtained a topological semimetal. Its semimetalicity is intricately linked to the non-Abelian nature of the translation group in hyperbolic space. These results show that hyperbolic space holds many surprises, of which even more can be expected beyond the non-interacting regime I discuss.