Surface plasmons for doped graphene

Within the Dirac model for the electronic excitations of graphene, we calculate the full polarization tensor with finite mass and chemical potential. It has, besides the (00)-component, a second form factor, which must be accounted for. We obtain explicit formulas for both form factors and for the reflection coefficients. Using these, we discuss the regions in the momentum-frequency plane where plasmons may exist and give numeric solutions for the plasmon dispersion relations. It turns out that plasmons exist for both, TE and TM polarizations over the whole range of the ratio of mass to chemical potential, except for zero chemical potential, where only a TE plasmon exists.