title: Lobachevsky crystallography made real through carbon pseudospheres.
abstract: We realize Lobachevsky geometry in a simulation lab, by producing a carbon-based energetically stable molecular structure, arranged in the shape of a Beltrami pseudosphere. We find that this structure: (i) corresponds to a non-Euclidean crystallographic group, namely a loxodromic subgroup of SL(2, Z); (ii) has an unavoidable singular boundary, that we fully take into account. Our approach, substantiated by extensive numerical simulations of Beltrami pseudospheres of different size, might be applied to other surfaces of constant negative Gaussian curvature, and points to a general procedure to generate them. Our results also pave the way to test certain scenarios of the physics of curved spacetimes owing to graphene's unique properties.
authors.affiliation: Faculty of Mathematics and Physics, Charles University in Prague, Prague, Czech Republic. European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT*), Bruno Kessler Foundation & Trento Institute for Fundamental Physics and Applications (TIFPA-INFN), Trento, Italy.
authors.forename: Simone
authors.initials: S
authors.lastname: Taioli
authors.forename: Ruggero
authors.initials: R
authors.lastname: Gabbrielli
authors.forename: Stefano
authors.initials: S
authors.lastname: Simonucci
authors.forename: Nicola Maria
authors.initials: NM
authors.lastname: Pugno
authors.forename: Alfredo
authors.initials: A
authors.lastname: Iorio