Orbital-Free Density Functional Theory of Out-of-Plane Charge Screening in Graphene

Jianfeng Lu, Vitaly Moroz, Cyrill B. Muratov

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


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 nonzero response at a finite threshold value of the external charge is proved.

Original languageEnglish (US)
Pages (from-to)1391-1430
Number of pages40
JournalJournal of Nonlinear Science
Issue number6
StatePublished - Dec 1 2015

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • General Engineering
  • Applied Mathematics


  • Fractional Laplacian
  • Ground state
  • Massless relativistic fermions
  • Non-linear response


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