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

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.

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Cited by in corpus (7)

• Frequency-dependent substrate screening of excitons in atomically thin transition metal dichalcogenide semiconductors
• Controlling plasmon modes and damping in buckled two-dimensional material open systems
• Dynamical screening effects of substrate phonons on two-dimensional excitons
• Tunable plasmon-enhanced second-order optical nonlinearity in transition metal dichalcogenide nanotriangles
• Graphene plasmons: impurities and nonlocal effects
• Numerically efficient density-matrix technique for modeling electronic transport in midinfrared quantum cascade lasers
• Partially coherent electron transport in terahertz quantum cascade lasers based on a Markovian master equation for the density matrix