Eur. Phys. J. B 73, 389-404 (2010)
https://doi.org/10.1140/epjb/e2010-00001-2

Scattering in graphene with impurities: A low energy effective theory

¹ Theory Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Calcutta 700064, India
² Rudjer Bošković Institute, Bijenička c.54, HR-10002 Zagreb, Croatia
³ School of Mathematical Sciences, UCD, Belfield, Dublin 4, Ireland
⁴ Department of Theoretical Physics, Indian Association for the Cultivation of Science, 700032 Calcutta, India

Corresponding author: asamsarov@irb.hr

Received: 20 September 2009
Revised: 9 November 2009
Published online: 15 January 2010

Abstract

We analyze the scattering sector of the Hamiltonians for both gapless and gapped graphene in the presence of a charge impurity using the 2D Dirac equation, which is applicable in the long wavelength limit. We show that for certain range of the system parameters, the combined effect of the short range interactions due to the charge impurity can be modelled using a single real parameter appearing in the boundary conditions. The phase shifts and the scattering matrix depend explicitly on this parameter. We argue that this parameter for graphene can be fixed empirically, through measurements of observables that depend on the scattering data.