Orbital-Free Density Functional Theory of Out-of-Plane Charge Screening in Graphene
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© 2015, Springer Science+Business Media New York.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.
Published Version (Please cite this version)10.1007/s00332-015-9259-4
Publication InfoLu, Jianfeng; Moroz, V; & Muratov, CB (2015). Orbital-Free Density Functional Theory of Out-of-Plane Charge Screening in Graphene. Journal of Nonlinear Science, 25(6). pp. 1391-1430. 10.1007/s00332-015-9259-4. Retrieved from http://hdl.handle.net/10161/14103.
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Associate Professor of Mathematics
Jianfeng Lu is an applied mathematician interested in mathematical analysis and algorithm development for problems from computational physics, theoretical chemistry, materials science and other related fields.More specifically, his current research focuses include:Electronic structure and many body problems; quantum molecular dynamics; multiscale modeling and analysis; rare events and sampling techniques.