Electrodynamics of Graphene in the presence of the Extrinsic Spin Hall Effect 米格爾 ^{1*}^{1}物理, 清華大學, 新竹, Taiwan* presenting author:Miguel A. Cazalilla, email:miguel.cazalilla@gmail.com We extend the electrodynamics of two dimensional electron gases to account for the extrinsic spin Hall effect (SHE). The theory is applied to doped graphene
decorated with a random distribution of absorbates that induce spin-orbit coupling (SOC) by proximity. The formalism extends previous semiclassical treatments of the SHE to the non-local dynamical regime. Within a particle-number conserving approximation, we derive the conductivity, dielectric function, and spin Hall angle in the small frequency and wave vector limit. The spin Hall is found to decrease with frequency, but remains comparable to its DC value around the frequency corresponding to the Drude peak. The plasmon dispersion and linewidth are obtained. Our result suggests an explanation for the rather similar plasmonic response of exfoliated graphene [e.g. Z. Fei \emph{et al.} Nature {\bf 487}, 82 (2012)], which does not exhibit the SHE, and graphene grown by chemical vapor deposition [e.g. J. Chen \emph{et al.} Nature {\bf 487}, 77 (2012)], for which a large SHE has been recently reported [J. Jayalakumar \emph{et al}. Nature communications {\bf 5}, 4748 (2014)]. Our theory also lies the foundation for the future experimental searches of SOC effects in the electrodynamic response of two-dimensional electron gases with SOC disorder. Keywords: Graphene, Spintronics, Plasmonics |