2010/08/04 by Cheol-Hwan Park, Liang Z. Tan, Liang Zheng Tan +1
Materials Science · Mathematics · Physics and Astronomy · #Brillouin zone #Carbon Nanotubes in Composites #Condensed matter physics #Dirac equation #Dirac fermion #Geometry #Graphene #Graphene research and applications #Group velocity #Magnetic field #Massless particle #Mathematics #Physics #Quantum and electron transport phenomena #Quantum mechanics #Relativistic wave equations #Scalar (mathematics) #Scalar potential #Vector potential #cond-mat.mtrl-sci
paper · pdf · doi:10.1016/j.physe.2010.07.022
published as Physica E, 43, 651-656 (2011) · 8 pages, 4 figures
openalex publication_date 2010/08/04 · arxiv created 2011/02/18 · arxiv updated 2011/02/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We discuss the novel electronic properties of graphene under an external periodic scalar or vector potential, and the analytical and numerical methods used to investigate them. When graphene is subjected to a one-dimensional periodic scalar potential, owing to the linear dispersion and the chiral (pseudospin) nature of the electronic states, the group velocity of its carriers is renormalized highly anisotropically in such a manner that the velocity is invariant along the periodic direction but is reduced the most along the perpendicular direction. Under a periodic scalar potential, new massless Dirac fermions are generated at the supercell Brillouin zone boundaries. Also, we show that if the strength of the applied scalar potential is sufficiently strong, new zero-energy modes may be generated. With the periodic scalar potential satisfying some special conditions, the energy dispersion near the Dirac point becomes quasi one-dimensional. On the other hand, for graphene under a one-dimensional periodic vector potential (resulting in a periodic magnetic field perpendicular to the graphene plane), the group velocity is reduced isotropically and monotonically with the strength of the potential.