Surface plasmons for doped graphene

TL;DR

This paper calculates the polarization tensor of doped graphene within the Dirac model, deriving formulas for plasmon dispersion relations and identifying conditions for TE and TM plasmon existence.

Contribution

It provides explicit formulas for the polarization tensor components and reflection coefficients, advancing understanding of plasmon behavior in doped graphene.

Findings

Plasmons exist for both TE and TM polarizations across most conditions.

TE plasmons exist at zero chemical potential, but TM plasmons do not.

Explicit dispersion relations for graphene plasmons are derived.

Abstract

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.