Hyperbolic non-Abelian semimetal

TL;DR

This paper explores topologically protected semi-metallic band crossings in hyperbolic lattices, revealing unique non-Abelian Bloch states, a high-dimensional reciprocal space, and a topologically protected nodal manifold characterized by a second Chern number.

Contribution

It introduces the concept of hyperbolic non-Abelian semimetals, extending topological band theory to negatively curved lattices with non-Abelian Bloch states and high-dimensional reciprocal space.

Findings

Unconventional scaling in the density of states at low energies

Identification of a topologically protected nodal manifold of codimension five

Characterization of the nodal manifold by a second Chern number

Abstract

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, such lattices are associated with a high-dimensional reciprocal space. In addition, they support non-Abelian Bloch states which, unlike conventional Bloch states, acquire a matrix-valued Bloch factor under lattice translations. Combining diverse numerical and analytical approaches, we uncover an unconventional scaling in the density of states at low energies, and illuminate a nodal manifold of codimension five in the reciprocal space. The nodal manifold is topologically protected by a nonzero second Chern number, reminiscent of the characterization of Weyl nodes by the first Chern number.