Hi,
We all know the dispersion relation for an ideal graphene in hexagonal lattice. Since graphene is polycrystalline by nature, assuming a perfect graphene crystals with average size La, nm connected by pentagons and heptagons randomly distributed in their edges, what will be the dispersion relation of such material? Can we theoretically quantify the effect of the domain size on the dispersion relation? Is there experimental evidences ?
For example in CVD graphene transferred onto SiO2 substrates, the bulk graphene resistivity ρ, was measured by the four-point probe technique and correlated to crystallite size La by Vlassiouk et al. [1] through the following equation:
ρ(Ω)=6.7105/La (nm)
Another method of estimating the conductivity of arbitrarily stacked graphene sheets was proposed from semi-classical Boltzmann transport theory could be found here [2-4].
Thanks,
{1} Vlassiouk, I.; Smirnov, S.; Ivanov, I.; Fulvio, P.F.; Dai, S.; Meyer, H.; Chi, M.; Hensley, D.; Datskos, P.; Lavrik, N.V. Electrical and thermal conductivity of low temperature CVD graphene: The effect of disorder. Nanotechnology 2011, 22, 275716. [Google Scholar] [CrossRef] [PubMed]
{2} Min, H.; Jain, P.; Adam, S.; Stiles, M.D. Semiclassical Boltzmann transport theory for graphene multilayers. Phys. Rev. B 2011, 83, 195117. [Google Scholar] [CrossRef]
{3} Chen, J.H.; Cullen, W.G.; Jang, C.; Fuhrer, M.S.; Williams, E.D. Defect scattering in graphene. Phys. Rev. Lett. 2009, 102, 236805. [Google Scholar] [CrossRef] [PubMed]
{4} Stauber, T.; Peres, N.M.R.; Guinea, F. Electronic transport in graphene: A semiclassical approach including midgap states. Phys. Rev. B 2007, 76, 205423. [Google Scholar] [CrossRef]
you may be interested with this paper
Scattering of graphene plasmons at abrupt
interfaces: an analytic and numeric study
Tank you Nwar for suggesting the paper
Scattering of graphene plasmons at abrupt interfaces: An analytic and numeric study
A. J. Chaves, B. Amorim, Yu. V. Bludov, P. A. D. Gonçalves, and N. M. R. Peres
Phys. Rev. B 97, 035434 – Published 23 January 2018
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