2015/04/30 by Pedro Roman-Taboada, Pedro Roman‐Taboada, Gerardo G. Naumis · 13 citations
Materials Science · Mathematics · Physics and Astronomy · #Atomic orbital #Biorthogonal system #Condensed matter physics #Degenerate energy levels #Electron #Energy spectrum #Geometry #Graphene #Graphene research and applications #Hamiltonian (control theory) #Mathematics #Periodic potential #Physics #Quantum and electron transport phenomena #Quantum mechanics #Quasiperiodic function #Ripple #Topological Materials and Phenomena #Zigzag #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevb.92.035406
published in Physical Review B 92(3) (American Physical Society) · 8 pages, 7 figures
openalex publication_date 2015/07/06 · arxiv created 2015/07/21 · openalex created_date 2016/06/24 · arxiv updated 2017/07/26 · openalex updated_date 2026/08/05
We report an exact map into one-dimensional effective chains of the tight-binding Hamiltonian for electrons in armchair and zigzag graphene nanoribbons with any uniaxial ripple. This mapping is used for studying the effect of uniaxial periodic ripples, taking into account the relative orientation changes between \ensuremathπ orbitals. Such effects are important for short-wavelength ripples, while for long-wave ones, the system behaves nearly as strained graphene. The spectrum has a complex nature, akin to the Hofstadter butterfly with a rich localization behavior. Gaps at the Fermi level and dispersionless bands were observed, as well. The complex features of the spectrum arise as a consequence of the quasiperiodic or periodic nature of the effective one-dimensional system. Some features of these systems can be understood by considering weakly coupled dimers. The eigenenergies of such dimers are highly degenerate, and the net effect of the ripple can be seen as a perturbation potential that splits the energy spectrum. Several particular cases were analytically solved to understand this feature.