2007/06/30 by Dmitry S. Novikov, D. S. Novikov · 258 citations
Materials Science · Physics and Astronomy · #Condensed matter physics #Coulomb #Dirac (video compression format) #Dirac equation #Dirac fermion #Elastic scattering #Electron #Graphene #Graphene research and applications #Massless particle #Neutrino #Phonon scattering #Physics #Quantum and electron transport phenomena #Quantum electrodynamics #Quantum mechanics #Scattering #Scattering theory #Topological Materials and Phenomena #cond-mat.mes-hall #cond-mat.mtrl-sci
paper · pdf · doi:10.1103/physrevb.76.245435
published in Physical Review B 76(24) (American Physical Society) · 17 pages, 4 figures. Published version
arxiv created 2007/12/28 · openalex publication_date 2007/12/28 · arxiv updated 2011/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Electron properties of graphene are described in terms of Dirac fermions. Here we thoroughly outline the elastic scattering theory for the two-dimensional massive Dirac fermions in the presence of an axially symmetric potential. While the massless limit is relevant for pristine graphene, keeping finite mass allows for generalizations onto situations with broken symmetry between the two sublattices and provides a link to the scattering theory of electrons in a parabolic band. We demonstrate that the Dirac theory requires short-distance regularization for potentials which are more singular than 1∕r. The formalism is then applied to scattering off a smooth short-ranged potential. Next, we consider the Coulomb potential scattering, where the Dirac theory is consistent for a point scatterer only for the effective impurity strength below 1∕2. From the scattering phase shifts we obtain the exact Coulomb transport cross section in terms of the impurity strength. The results are relevant for transport in graphene in the presence of impurities that do not induce scattering between the Dirac points in the Brillouin zone.