Dielectric function and plasmons in graphene: A self-consistent-field calculation within a Markovian master equation formalism

TL;DR

This paper presents a self-consistent-field method within a Markovian master equation formalism to accurately compute the dielectric function and plasmons in graphene, accounting for multiple scattering mechanisms and substrate effects.

Contribution

The authors develop a novel SCF-MMEF approach that captures interband and intraband scattering in nanostructures with arbitrary band dispersion, applied here to graphene.

Findings

Plasmon propagation lengths are on the order of tens of nanometers.

Plasmon suppression occurs below the highest surface phonon energy on polar substrates.

Propagation lengths improve with fewer impurities, lower temperatures, and higher carrier densities.

Abstract

We introduce a method for calculating the dielectric function of nanostructures with an arbitrary band dispersion and Bloch wave functions. The linear response of a dissipative electronic system to an external electromagnetic field is calculated by a self-consistent-field approach within a Markovian master equation formalism (SCF-MMEF) coupled with full-wave electromagnetic equations. The SCF-MMEF accurately accounts for several concurrent scattering mechanisms. The method captures interband electron-hole-pair generation, as well as the interband and intraband electron scattering with phonons and impurities. We employ the SCF-MMEF to calculate the dielectric function, complex conductivity, and loss function for supported graphene. From the loss-function maximum, we obtain plasmon dispersion and propagation length for different substrate types [nonpolar diamondlike carbon (DLC) and polar SiO$_2$ and hBN], impurity densities, carrier densities, and temperatures. Plasmons on the two polar substrates are suppressed below the highest surface phonon energy, while the spectrum is broad on the nonpolar DLC. Plasmon propagation lengths are comparable on polar and nonpolar substrates and are on the order of tens of nanometers, considerably shorter than previously reported. They improve with fewer impurities, at lower temperatures, and at higher carrier densities.