Hyperbolic Band Theory


Seminar Link: Picoelectrodynamics Theory Network - YouTube


Hyperbolic lattices are a new form of synthetic quantum matter in which particles effectively hop on a discrete tiling of two-dimensional hyperbolic space, a non-Euclidean space of negative curvature. Hyperbolic tilings were studied by the geometer H.S.M. Coxeter and popularized through art by M.C. Escher. Recent experiments in circuit quantum electrodynamics and electric circuit networks have demonstrated the coherent propagation of wave-like excitations on hyperbolic lattices. While the familiar band theory of solids adequately describes wave propagation through periodic media in Euclidean space, it is unclear how concepts like crystal momentum and Bloch waves can be extended to hyperbolic space. In this talk, I will discuss a generalization of Bloch's band theory for hyperbolic lattices and stress the intriguing connections it establishes between condensed matter physics, high-energy physics, and pure mathematics.

By Prof. Joseph Maciejko

Dr. Joseph Maciejko is an associate professor in the Department of Physics, Canada Research Chair in Condensed Matter Theory, and the director of the Theoretical Physics Institute at the University of Alberta in Edmonton, Canada. He graduated from McGill University with an M.Sc. in Physics in 2006 and from Stanford University with a Ph.D. in Physics in 2011. He is the recipient of the Research Award from the Faculty of Science in 2020, the Great Supervisor Award from the Faculty of Graduate Studies and Research in 2020, and the Student's Choice Award from the Faculty of Science in 2018 from the University of Alberta. He has a wide range of research interests in theoretical condensed matter physics including emergent phenomena in quantum many-body systems; topological phases of matter including topological insulators, superfluids, and superconductors and the quantum Hall effect; quantum transport in low-dimensional systems and semiconductor physics; fractionalization and strongly correlated systems; field theories of many-body systems and connections between condensed matter physics and high-energy physics.