Dynamical Polarizability of Graphene with Spatial Dispersion

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.

10 pages, 6 figures

References in corpus (19)

• Electric Field Effect in Atomically Thin Carbon Films
• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• The electronic properties of graphene
• Advanced capabilities for materials modelling with Quantum ESPRESSO
• Dielectric function, screening, and plasmons in 2D graphene
• Optical properties of graphene
• Dynamical polarization of graphene at finite doping
• Space-time dispersion of graphene conductivity
• Unusual Microwave Response of Dirac Quasiparticles in Graphene
• AC conductivity of graphene: from tight-binding model to 2+1-dimensional quantum electrodynamics
• Screening induced temperature dependent transport in 2D graphene
• Near-field heat transfer between graphene/hBN multilayers
• Extraordinary nonlinear plasmonics in graphene nanoislands
• Ultrafast Radiative Heat Transfer
• Dynamics of the particle - hole pair creation in graphene
• Graphene-based thermal repeater
• Strong thermal and electrostatic manipulation of the Casimir force in graphene multilayers
• Conductivity of graphene in the framework of Dirac model: Interplay between nonzero mass gap and chemical potential
• Quantum electrodynamic approach to the conductivity of gapped graphene

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• Temperature Dependence of the Response Functions of Graphene: Impact on Casimir and Casimi-Polder Forces in and out of Thermal Equilibrium
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