Fig. 2. Temperature dependence of the plasmon dispersion relation.

We plot the squared Fresnel reflection coefficient ${\left|r\right|}^2$ for p polarization as a function of the photon energy ħω and in-plane wave vector $k_{\parallel }$ for three different configurations: a graphene, b graphene/silver and c graphene/spacer/silver films, all of which are supported on a dielectric substrate (ε = 2), as shown in the lower insets. The silver layer thickness is 1 nm in b and 2 nm in c (i.e., approximately 4 and 8 (111) atomic layers, respectively⁴²). The spacer in c has ε = 2 and 1-nm thickness. We consider three different values of the electron temperature T_e in graphene (top to bottom, see labels), while the metal electrons and the lattices of all materials are kept at room temperature T₀ = 300 K. Graphene is doped to E_F = 0.55 eV in all cases. Light ($\omega =k_{\parallel }c$, blue) and Fermi ($\omega =k_{\parallel }{v}_F$, red) lines are shown for reference