Flat bands and band-touching from real-space topology in hyperbolic lattices

Abstract

Hopping models on geometrically frustrated lattices, such as the kagome and dice lattices, exhibit perfectly flat energy bands that result from eigenstates localized along contractible and/or noncontractible real-space loops. The degeneracy of such flat bands has been understood from an interplay of real-space topology and momentum-space band theory. Here, the authors generalize this paradigm to frustrated hyperbolic lattices, including those realized in recent circuit quantum electrodynamics experiments. They show that hyperbolic flat-band characteristics can similarly be understood by combining real-space topology arguments with the recently developed hyperbolic band theory.

Locations

• Physical review. B./Physical review. B - View
• arXiv (Cornell University) - View - PDF
• DataCite API - View