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Effects of substrate and graphene surface roughness on graphene sheet plasmons

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Lyon K., Miškovic Z. L.
Nanoscale Systems: Mathematical Modeling, Theory and Applications
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2014
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tom 3
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nr 1
EN
We study the effects of roughness in a graphene layer that lies on a substrate with rough surface on the dynamic response of such a structure. Using an analytical expression for the dielectric function of flat graphene in the optical limit allows us to tackle the effects of roughness on the sheet plasmon in graphene. We first formulate a stochastic eigenvalue problem for the plasmon dispersion in terms of the roughness parameters that include both the auto– and the cross–correlation functions of graphene and the substrate surfaces. Using the projection operator methodwe reduce this problem to an integral equation for an effective dielectric function of graphene,which implies the existence of plasmon damping due to the roughness effects.
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Analyzing nonlocal effects in the plasmon spectra of a metal slab by the Green’s function technique for hydrodynamic model

71%
Kang N., Miškovic Z. L., Zhang Y.-Y., Song Y.-H., Wang Y.-N.
Nanoscale Systems: Mathematical Modeling, Theory and Applications
|
2014
|
tom 3
|
nr 1
EN
We study the dynamic response of a metal slab containing electron gas described by the hydrodynamic model with dispersion. The resulting wave equation for the perturbed electron density is solved by means of the Green’s function that satisfies Neumann boundary conditions at the endpoints of the slab. This solution is coupled with the electrostatic potential, which is expressed in terms of the Green’s function for the Poisson equation for a layered structure consisting of three dielectric regions. As an illustration, a set of dispersion relations for eigenfrequencies is deduced for the plasma oscillations in the electron gas, corresponding to both the surface and the bulk modes of even and odd symmetry with respect to the center of the metal slab.
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