Hyperbolic Topological Band Insulators

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 hyp...

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Bibliographic Details
Published in:Physical review letters 2022-12, Vol.129 (24), p.246402-246402, Article 246402
Main Authors: Urwyler, David M, Lenggenhager, Patrick M, Boettcher, Igor, Thomale, Ronny, Neupert, Titus, Bzdušek, Tomáš
Format: Article
Language:English
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Summary: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 nontrivial 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 modeling propagation of edge excitations, and by their robustness against disorder.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.129.246402