2010/05/31 by Keith R. Dienes, Brooks Thomas
Engineering · Materials Science · Mathematics · Physics and Astronomy · #Advancements in Battery Materials #Algorithm #Basis (linear algebra) #Carbon Nanotubes in Composites #Carbon fibers #Computer science #Geometry #Graphene research and applications #Homogeneous space #Isospectral #Mathematics #Modular design #Physics #Pure mathematics #Theoretical physics #cond-mat.mes-hall #hep-th #math-ph #math.MP
paper · pdf · doi:10.1103/physrevb.84.085444
published as Phys.Rev.B84:085444,2011 · 12 pages, ReVTeX, 6 figures, 1 table. Replaced to match published version
openalex publication_date 2011/08/29 · arxiv created 2011/08/30 · arxiv updated 2011/09/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Recently there has been considerable interest in the properties of carbon nanotori. Such nanotori can be parametrized according to their radii, their chiralities, and the twists that occur upon joining opposite ends of the nanotubes from which they are derived. In this paper, however, we demonstrate that many physically distinct nanotori with wildly different parameters nevertheless share identical band structures, energy spectra, and electrical conductivities. This occurs as a result of certain geometric symmetries known as modular symmetries, which are direct consequences of the properties of the compactified graphene sheet. Using these symmetries, we show that there is a dramatic reduction in the number of spectrally distinct carbon nanotori compared with the number of physically distinct carbon nanotori. The existence of these modular symmetries also allows us to demonstrate that many statements in the literature concerning the electronic properties of nanotori are incomplete because they fail to respect the spectral equivalences that follow from these symmetries. We also find that as a result of these modular symmetries, the fraction of spectrally distinct nanotori which are metallic is approximately three times greater than would naively be expected on the basis of standard results in the literature. Finally, we demonstrate that these modular symmetries also extend to cases in which our carbon nanotori enclose nonzero magnetic fluxes.