Dynamical Polarizability of Graphene with Spatial Dispersion

TL;DR

This paper analyzes the electronic polarizability of graphene using various theoretical methods, comparing their accuracy and applicability, and providing insights into the effects of doping and temperature on graphene's screening properties.

Contribution

It systematically compares multiple theoretical approaches for graphene's polarizability, validating the tight-binding method against ab initio calculations and deriving analytical formulas for different regimes.

Findings

Tight-binding method matches ab initio results for polarizability.

Dirac model reproduces tight-binding results below 3 eV.

Intra-band transitions dominate at low energies in doped graphene.

Abstract

We perform a detailed analysis of electronic polarizability of graphene with different theoretical approaches. From Kubo's linear response formalism, we give a general expression of frequency and wave-vector dependent polarizability within the random phase approximation. Four theoretical approaches have been applied to the single-layer graphene and their differences are on the band-overlap of wavefunctions. By comparing with the \textit{ab initio} calculation, we discuss the validity of methods used in literature. Our results show that the tight-binding method is as good as the time-demanding \textit{ab initio} approach in calculating the polarizability of graphene. Moreover, due to the special Dirac-cone band structure of graphene, the Dirac model reproduces results of the tight-binding method for energy smaller than \SI{3}{\electronvolt}. For doped graphene, the intra-band transitions dominate at low energies and can be described by the Lindhard formula for two-dimensional electron gases. At zero temperature and long-wavelength limit, with the relaxation time approximation, all theoretical methods reduce to a long-wave analytical formula and the intra-band contributions agree to the Drude polarizability of graphene. Effects of electrical doping and temperature are also discussed. This work may provide a solid reference for researches and applications of the screening effect of graphene.