Speaker
Description
We introduce the theory and experimental realization of hyperbolic matter, a novel state of matter in curved space that contradicts our Euclidean geometric intuition. It is made of particles moving in the infinite two-dimensional hyperbolic plane. Curvature of space is emulated through a hyperbolic lattice using topolectric circuit networks relying on a newly developed complex-phase circuit element. For a first example, we experimentally realize hyperbolic graphene as an example of topologically nontrivial hyperbolic matter and compare measurements of Dirac particles and Berry curvature to predictions from band theory. As a second example of topological hyperbolic matter, we theoretically discuss Haldane models and Chern insulators on hyperbolic lattices. Our work sets the stage to realize interacting and quantum hyperbolic matter to challenge our established theories of Physics in curved space.
