Elastic scattering theory and transport in graphene
By Dmitry S. Novikov. 2007
160 citations recorded by the source corpus.
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.
Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry
View Paper: https://www.semanticscholar.org/paper/10034a0a96828d5b4d806dd203da555c45b2ea5c
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In Atomic and Molecular Physics, and Optics
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Citations in the corpus
- The electronic properties of graphene (2007, methodology): “Thesolution of the Dira equation for the Coulomb poten-tial in 2D an be studied analyti ally (Biswas et al.,2007; DiVin enzo and Mele, 1984; Novikov, 2007a;Pereira et al., 2007b; Shytov et al., 2007).”
- Electronic transport in two-dimensional graphene (2010, background): “In the context of graphene the problem was first studied by Divincenzo and Mele (1984) and recently more in detail by several authors (Biswas et al., 2007; Fistul and Efetov, 2007; Fogler et al., 2007; Novikov, 2007b; Pereira et al., 2007; Shytov et al., 2007a,b; Terekhov et al., 2008).”
- Colloquium: The transport properties of graphene: An introduction (2010, methodology): “The same happens with the 2D Dirac equation (Lin, 1999; Novikov, 2007a; Pereira et al., 2007; Shytov et al., 2007).”