English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Recently there has been considerable interest in the properties of carbonnanotori. Such nanotori can be parametrized according to their radii, theirchiralities, and the twists that occur upon joining opposite ends of thenanotubes from which they are derived. In this paper, however, we demonstratethat many physically distinct nanotori with wildly different parametersnevertheless share identical band structures, energy spectra, and electricalconductivities. This occurs as a result of certain geometric symmetries knownas modular symmetries which are direct consequences of the properties of thecompactified graphene sheet. Using these symmetries, we show that there is adramatic reduction in the number of spectrally distinct carbon nanotoricompared with the number of physically distinct carbon nanotori. The existenceof these modular symmetries also allows us to demonstrate that many statementsin the literature concerning the electronic properties of nanotori areincomplete because they fail to respect the spectral equivalences that followfrom these symmetries. We also find that as a result of these modularsymmetries, the fraction of spectrally distinct nanotori which are metallic isapproximately three times greater than would naively be expected on the basisof standard results in the literature. Finally, we demonstrate that thesemodular symmetries also extend to cases in which our carbon nanotori enclosenon-zero magnetic fluxes.

Isospectral But Physically Distinct: Modular Symmetries and their Implications for Carbon Nanotori