Permittivity

graphenemodeling.graphene.monolayer.Permittivity(q, omega, FermiLevel, T, gamma, epsR, model=None)

Returns the in-plane permittivity of graphene.

Parameters:

• q (array-like, rad/m) – Wavenumber
• omega (array-like, rad/s) – Angular frequency
• epsR (scalar, unitless) – background relative permittivity

Notes

Permittivity relates to the scalar optical conductivity through the expression

\[\epsilon(q, \omega) = \epsilon_0 + \frac{i\sigma(q,\omega)}{\omega}\]

At \(\omega=0\), we can use the expression found in Ref. 2,

\[\epsilon(q) = \kappa^* + \frac{2\pi e^2}{\kappa q}\Pi^+(q)\]

References

[1] “Lumerical: Modeling Methodology.” n.d. Accessed April 1, 2019.

https://apps.lumerical.com/other_application_graphene_simulation_tips.html.

[2] Hwang, E.H., and Das Sarma, S. (2007). Dielectric function, screening, and plasmons in two-dimensional graphene. Phys. Rev. B 75, 205418. https://link.aps.org/doi/10.1103/PhysRevB.75.205418.