Nonlinear screening of external charge by doped graphene

graphene;nonlinear screening;doped graphene;Thomas Fermi model;Applied Mathematics

Ghaznavi, Mahmoudreza

University of Waterloo

关键词: graphene;    nonlinear screening;    doped graphene;    Thomas Fermi model;    Applied Mathematics;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/5098/1/Ghaznavi_Mahmoudreza.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

In therst part of this thesis we discuss some details of properties of grapheneand we explain the tight-binding approach tond the energy spectrum in graphene.In the second part of the thesis, we solve a nonlinear integral equation for the electrostaticpotential in doped graphene due to an external charge, arising from aThomas-Fermi (TF) model for screening by graphene;;s electron bands. In particular,we study the e ects of anite equilibrium charge carrier density in graphene,non-zero temperature, non-zero gap between graphene and a dielectric substrate,as well as the nonlinearity in the band density of states. E ects of the exchangeand correlation interactions are also briey discussed for undoped graphene at zerotemperature. Results from the nonlinear model are compared with results fromboth the linearized TF model and the dielectric screening model within the randomphase approximation (RPA). In addition, the image potential of the external chargeis evaluated from the solution of the nonlinear integral equation and compared tothe results of linear models. We have found generally good agreement between theresults of the nonlinear TF model and the RPA model in doped graphene, apartfrom Friedel oscillations in the latter model. However, relatively strong nonlineare ects in the TF model are found to persist even at high doping densities and largedistances of the external charge.