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

We report an exact map into one dimensional effective chains, of thetight-binding Hamiltonian for electrons in armchair and zigzag graphenenanoribbons with any uniaxial ripple. This mapping is used for studying theeffect of uniaxial periodic ripples, taking into account the relativeorientation changes between $\pi$ orbitals. Such effects are important forshort wavelength ripples, while for long-wave ones, the system behaves nearlyas strained graphene. The spectrum has a complex nature, akin to the Hofstadterbutterfly with a rich localization behavior. Gaps at the Fermi level anddispersionless bands were observed, as well. The complex features of thespectrum arise as a consequence of the quasiperiodic or periodic nature of theeffective one dimensional system. Some features of these systems areunderstandable by considering weakly coupled dimers. The eigenenergies of suchdimers are highly degenerated and the net effect of the ripple can be seen as aperturbation potential that splits the energy spectrum. Several particularcases were analytically solved to understand such feature.

Spectral butterfly and electronic localization in rippled-graphene nanorribons: mapping onto effective one-dimensional chains