Crystallography of hyperbolic lattices

Abstract

Hyperbolic lattices are intricately wired networks that constitute an exciting experimental platform for tabletop simulations of physical models in synthetic negatively curved spaces. This work reveals a hidden crystal order underneath the labyrinthine beauty of such lattices - an order made of unit cells arranged periodically onto the scaffold of a hyperbolic Bravais lattice. This sets the stage for applying powerful techniques from crystallography and band theory to describe experiments in circuit quantum electrodynamics and topoelectrical circuit networks as well as to search for novel phases of matter.