Screening in Graphene: Response to External Static Electric Field and an Image-Potential Problem

Abstract

We present a detailed first-principles investigation of the response of a free-standing graphene sheet to an external perpendicular static electric field E. The charge density distribution in the vicinity of the graphene monolayer that is caused by E was determined using the pseudopotential density-functional theory approach. Different geometries were considered. The centroid of this extra density induced by an external electric field was determined as zim = 1.048 Å at vanishing E, and its dependence on E has been obtained. The thus determined zim was employed to construct the hybrid one-electron potential which generates a new set of energies for the image-potential states.

Growth and local electronic properties of Cobalt nanodots underneath graphene on SiC(0001)

“…4) is asymmetric and so must be fitted by two Lorentzian profiles (we obtain similar results with Gaussian or Voigt profiles), we label those features (0 + , 0 − ) (and 1 + , 1 − in Fig. 4d) to remember that IPS theoretical calculations of freestanding monolayer graphene [76,77] have proposed splitting of each IPS in couple indexed n ± corresponding to the even or odd symmetry of those states relative to the geometric graphene plane. We choose this notation following the literature [35,75].…”

Cytotoxicity of Carbon Nanotubes, Graphene, Fullerenes, and Dots

“…The diagnostic method, bioimaging, is connected with the penetration of drugs and diagnostic agents into tissues and cells and the sensitivity of detection. Bioimaging is controlled by biodegradability, biocompatibility, specificity, and applicability for carbon nanotubes [68][69][70][71][72][73][74][75][76][77][78][79][80][81], graphene [82][83][84][85][86][87][88][89][90][91][92][93][94], fullerenes [95], and dots [96].…”

Application of a Fluctuating Charge Polarization Model to Large Polyaromatic Hydrocarbons and Graphene Nanoflakes

“…It is well-known that an improved description of the polarization potential resulting from a point charge interacting with a conducting sheet includes a shift in the “image plane” which accounts for the displacement of the charge distribution outside the plane of atoms. − This image plane shift results in a − Q 2 /(4| z – sgn­( z ) × z im |) potential, where z im gives the location of the image plane, and sgn­( z ) is included to reflect the fact that the systems of interest are isolated and are symmetric with respect to reflection in the xy plane. In a recent study a value of z im = 1.98 a 0 was deduced for the image plane of graphene . Obviously, an FQ model allowing only in-plane charge redistribution cannot account for the image plane shift.…”

“…In a recent study a value of z im = 1.98 a 0 was deduced for the image plane of graphene. 48 Obviously, an FQ model allowing only in-plane charge redistribution cannot account for the image plane shift. However, the full MMÅ2 model, including both point inducible dipoles and charge flow terms, can partially account for this effect.…”

“… Polarization potential due to a negative point charge ( Q = −1) interacting with a grounded ( Q mol = +1) C 60000 nanoflake, as described by the full MMÅ2 model with both charge flow and inducible dipoles. The shifted-plane classical image potential is included for reference with the image plane parameter set to z im = 1.98 a 0 , as determined in ref ( 48 ). A fit of the polarization potential from the MMÅ2 model to a function of the form −6.8028/| z – b |, where b is a free parameter, is reported.…”