Density-Functional Theory of Graphene Sheets

Abstract

We outline a Kohn-Sham-Dirac density-functional-theory (DFT) scheme for graphene sheets that treats slowly-varying inhomogeneous external potentials and electron-electron interactions on an equal footing. The theory is able to account for the the unusual property that the exchange-correlation contribution to chemical potential increases with carrier density in graphene. Consequences of this property, and advantages and disadvantages of using the DFT approach to describe it, are discussed. The approach is illustrated by solving the Kohn-Sham-Dirac equations self-consistently for a model random potential describing charged point-like impurities located close to the graphene plane. The influence of electron-electron interactions on these non-linear screening calculations is discussed at length, in the light of recent experiments reporting evidence for the presence of electron-hole puddles in nearly-neutral graphene sheets.

11 pages, 9 figures, submitted. High-quality figures can be requested to the authors

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Cited by in corpus (56)

• Electronic transport in two dimensional graphene
• Electron-Electron Interactions in Graphene: Current Status and Perspectives
• Colloquium: The transport properties of graphene: An introduction
• Origin of Spatial Charge Inhomogeneity in Graphene
• Electron-electron interactions and doping dependence of the two-phonon Raman intensity in graphene
• Engineering artificial graphene in a two-dimensional electron gas
• Theory of thermopower in 2D graphene
• Ground-state of graphene in the presence of random charged impurities
• The quantum scattering time and its implications on scattering sources in graphene
• The quantum scattering time and its implications on scattering sources in graphene (Supplementary)
• The effective fine structure constant of freestanding graphene measured in graphite
• Epitaxial Graphene Electronic Structure And Transport
• Electron-hole puddles in the absence of charged impurities
• Linear response of doped graphene sheets to vector potentials
• Theory of charged impurity scattering in two dimensional graphene
• Electron density distribution and screening in rippled graphene sheets
• Finite-temperature Screening and the Specific Heat of Doped Graphene Sheets
• Effective medium theory for disordered two-dimensional graphene
• Many-body effects in van der Waals-Casimir interaction between graphene layers
• First-principles Theory of Nonlocal Screening in Graphene
• Universal conductance fluctuations in Dirac materials in the presence of long-range disorder
• Electron-electron interactions in decoupled graphene layers
• Variational approach to the excitonic phase transition in graphene
• Local and Global Screening Properties of Graphene Revealed through Landau Level Spectroscopy
• Linear Response and the Thomas-Fermi Approximation in Undoped Graphene
• Inhomogenous electronic structure, transport gap, and percolation threshold in disordered bilayer graphene
• Signatures of Klein tunneling in disordered graphene p-n-p junctions
• Interlayer excitonic superfluidity in graphene
• Two-dimensional metal-insulator-transition as a potential fluctuation driven semiclassical transport phenomenon
• Plasmonic physics of 2D crystalline materials
• Two-dimensional electronic transport on the surface of 3D topological insulators
• Artifical atoms in interacting graphene quantum dots
• The effect of sublattice symmetry breaking on the electronic properties of a doped graphene
• Ground state of graphene heterostructures in the presence of random charged impurities
• The Ground State of Graphene and Graphene Disordered by Vacancies
• Density fluctuation effects on the exciton condensate in double layer graphene
• Non-linear screening of external charge by doped graphene
• Magnetic Phases of Graphene Nanoribbons under Potential Fluctuations
• A comprehensive study of electric, thermoelectric and thermal conductivities of Graphene with short range unitary and charged impurities
• Orbital-free density functional theory of out-of-plane charge screening in graphene
• Quantum capacitance and compressibility of graphene: The role of Coulomb interactions
• Origin of the quasi-universality of the graphene minimal conductivity
• The saddle-point exciton signature on high harmonic generation in 2D hexagonal nanostructures
• Spin polarization and g-factor enhancement in graphene nanoribbons in magnetic field
• Klein Tunneling in the presence of random impurities
• Electronic structure of graphene-nanoribbons on hexagonal boron nitride
• First-principles multiscale modelling of charged adsorbates on doped graphene
• Scale-invariant puddles in Graphene: Geometric properties of electron-hole distribution at the Dirac point
• Graphene zigzag ribbons, square lattice models and quantum spin chains
• Inhomogeneity and nonlinear screening in gapped bilayer graphene
• Temperature dependence of the paramagnetic spin susceptibility of doped graphene
• Generalized virial theorem for massless electrons in graphene and other Dirac materials
• SUSY design of smooth quantum rings in graphene
• Scaling properties of mono-layer graphene away from the Dirac point
• Photoinduced polarization enhancement in biased bilayer graphene in the Landau level regime
• Particle-hole symmetry broken solutions in graphene nanoribbons: a multi-orbital, mean-field perspective