Hyperbolic Topological Band Insulators
Abstract
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 structure in a four- (or higher-)dimensional momentum space. To explore the uncharted topological aspects arising in hyperbolic band theory, we here introduce elementary models of hyperbolic topological band insulators: the hyperbolic Haldane model and the hyperbolic Kane-Mele model; both obtained by replacing the hexagonal cells of their Euclidean counterparts by octagons. Their non-trivial topology is revealed by computing topological invariants in both position and momentum space. The bulk-boundary correspondence is evidenced by comparing bulk and boundary density of states, by modelling propagation of edge excitations, and by their robustness against disorder.
Cite
@article{arxiv.2203.07292,
title = {Hyperbolic Topological Band Insulators},
author = {David M. Urwyler and Patrick M. Lenggenhager and Igor Boettcher and Ronny Thomale and Titus Neupert and Tomáš Bzdušek},
journal= {arXiv preprint arXiv:2203.07292},
year = {2023}
}
Comments
main text (4 pages incl. 5 figures and 1 table) + references + supplementary material (24 pages incl. 13 figures and 2 tables)