We review the basic theory of Friedel oscillations around a well localized impurity using Green's function technique in Born approximation. After a pedagogical presentation of the case of free electrons in various dimensions, we turn our attention to graphene, which is described by a tight-binding scheme. Utilizing the localized nature of the atomic wavefunctions we calculate the change in the electronic density due to the impurity, and identify, in addition to the slowly decaying long wavelength oscillations, a short wavelength pattern as well. The latter, being of opposite sign on the two sublattices of graphene, may cancel the leading inverse square envelope of the long wavelength oscillations, if a probe with resolution worse than a few unit cells is used. We corroborate these findings by exact diagonalization results on a 21×21 unit cell graphene sheet.
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics