Dielectric function, screening, and plasmons of graphene in the presence of spin-orbit interactions

TL;DR

This paper derives analytical expressions for the dielectric function, screening, and plasmon dispersion in graphene with arbitrary spin-orbit interactions, providing insights into their effects on electronic properties.

Contribution

It presents the first comprehensive analytical formulas for the polarization function and plasmon dispersion in graphene with general Rashba and intrinsic spin-orbit couplings.

Findings

Analytical expressions for real and imaginary parts of polarization function.

Asymptotic behavior of screened potential due to charged impurities.

Comparison of analytical and numerical plasmon dispersion results.

Abstract

We study the dielectric properties of graphene in the presence of Rashba and intrinsic spin-orbit interactions in their most general form, i.e., for arbitrary frequency, wave vector, doping, and spin-orbit coupling (SOC) parameters. The main result consists in the derivation of closed analytical expressions for the imaginary as well as for the real part of the polarization function. Several limiting cases, e.g., the case of purely Rashba or purely intrinsic SOC, and the case of equally large Rashba and intrinsic coupling parameters are discussed. In the static limit the asymptotic behavior of the screened potential due to charged impurities is derived. In the opposite limit ($q=0$, $\omega\to0$), an analytical expression for the plasmon dispersion is obtained and afterwards compared to the numerical result. Our result can also be applied to related systems such as bilayer graphene or topological insulators.