Graphene Electrodynamics in the presence of the Extrinsic Spin Hall Effect

TL;DR

This paper extends the electrodynamics of 2D electron gases to include the extrinsic spin Hall effect, analyzing its impact on conductivity, dielectric response, and plasmon behavior in doped graphene with spin-orbit coupling.

Contribution

It introduces a non-local dynamical formalism for the extrinsic spin Hall effect in graphene, providing new insights into its influence on plasmon dispersion and electrodynamic properties.

Findings

Spin Hall angle decreases with frequency and wave number but remains significant near the Drude peak.

Extrinsic SHE modifies plasmon dispersion at long wavelengths but not at large wave numbers.

The theory explains similar plasmonic responses in different graphene samples regardless of SHE presence.

Abstract

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 compute the conductivity, dielectric function, and spin Hall angle in the small frequency and wave vector limit. The spin Hall angle is found to decrease with frequency and wave number, but it remains comparable to its zero-frequency value around the frequency corresponding to the Drude peak. The plasmon dispersion and linewidth are also obtained. The extrinsic SHE affects the plasmon dispersion in the long wavelength limit, but not at large values of the wave number. This result suggests an explanation for the rather similar plasmonic response measured in exfoliated graphene, which does not exhibit the SHE, and graphene grown by chemical vapor deposition, for which a large SHE has been recently reported. Our theory also lays the foundation for future experimental searches of SOC effects in the electrodynamic response of two-dimensional electron gases with SOC disorder.