What is the Relationship Between Permitivity and Wave Vector in Graphene?

[Sadek]

i'm working on a project about the surface plasmon in graphene.
i found on some articles that we don't use Drude model to calculate permitivity on graphene but they didn't mention what's the right model !
can you help me please and give me the relation that link links between permitivity and wave vector in graphene and thanks

 

[Cryo]

I am not a specialist, but I would look to treat graphene as a surface, i.e. as a boundary condition, if I were you. Corresponingly, you don't want the dielectric constant - you want the surface conductivity (or surface dielectric constant, though this is not accepted as a term)

See https://aip.scitation.org/doi/abs/10.1063/1.2891452
Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene

Journal of Applied Physics 103, 064302 (2008); https://doi.org/10.1063/1.2891452
George W. Hansona)