Higher-order topological phases in crystalline and non-crystalline systems: a review Page 1
Journal of Physics: Condensed Matter ACCEPTED MANUSCRIPT • OPEN ACCESS Higher-order …

Topological band theory establishes a standardized framework for classifying different types
of topological matters. Recent investigations have shown that hyperbolic lattices in non …

The Laplace operator encodes the behavior of physical systems at vastly different scales,
describing heat flow, fluids, as well as electric, gravitational, and quantum fields. A key input …

Hyperbolic lattices are a new form of synthetic quantum matter in which particles effectively
hop on a discrete tessellation of two-dimensional (2D) hyperbolic space, a non-Euclidean …

Hyperbolic lattices are a revolutionary platform for tabletop simulations of holography and
quantum physics in curved space and facilitate efficient quantum error correcting codes …

Recently, hyperbolic lattices that tile the negatively curved hyperbolic plane emerged as a
new paradigm of synthetic matter, and their energy levels were characterized by a band …

A hyperbolic lattice allows for any p-fold rotational symmetry, in stark contrast to a two-
dimensional crystalline material, where only 2-fold, 3-fold, 4-fold, or 6-fold rotational …

We extend the notion of topologically protected semi-metallic band crossings to hyperbolic
lattices in a negatively curved plane. Because of their distinct translation group structure …

Topological photonics provides a new degree of freedom to robustly control electromagnetic
fields. To date, most of established topological states in photonics have been employed in …

Motivated by the recent experimental realizations of hyperbolic lattices in circuit quantum
electrodynamics and in classical electric-circuit networks, we study flat bands and band …