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arXiv · 2203.07292

Hyperbolic Topological Band Insulators

David M. Urwyler·Patrick M. Lenggenhager·Igor Boettcher·Ronny Thomale·Titus Neupert·Tomáš Bzdušek
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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.

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David M. Urwyler, Patrick M. Lenggenhager, Igor Boettcher, Ronny Thomale, Titus Neupert, Tomáš Bzdušek. 2023-01-08. Hyperbolic Topological Band Insulators. https://doi.org/10.1103/physrevlett.129.246402

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