Orbital-free density functional theory of out-of-plane charge screening in graphene

Abstract

We propose a density functional theory of Thomas-Fermi-Dirac-von Weizsäcker type to describe the response of a single layer of graphene resting on a dielectric substrate to a point charge or a collection of charges some distance away from the layer. We formulate a variational setting in which the proposed energy functional admits minimizers, both in the case of free graphene layers and under back-gating. We further provide conditions under which those minimizers are unique and correspond to configurations consisting of inhomogeneous density profiles of charge carrier of only one type. The associated Euler-Lagrange equation for the charge density is also obtained, and uniqueness, regularity and decay of the minimizers are proved under general conditions. In addition, a bifurcation from zero to non-zero response at a finite threshold value of the external charge is proved.

38 pages, 3 figures

References in corpus (13)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Dielectric function, screening, and plasmons in 2D graphene
• Interaction phenomena in graphene seen through quantum capacitance
• Vacuum Polarization and Screening of Supercritical Impurities in Graphene
• Chirality and Correlations in Graphene
• Nonlinear screening of charge impurities in graphene
• Nonlinear screening and ballistic transport in a graphene p-n junction
• Screening of a hypercritical charge in graphene
• Density-Functional Theory of Graphene Sheets
• Interaction corrections to the polarization function of graphene
• Electronic compressibility of graphene: The case of vanishing electron correlations and the role of chirality
• Stability of atoms and molecules in an ultrarelativistic Thomas-Fermi-Weizsaecker model

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