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 Matem. Mod., 2020, Volume 32, Number 8, Pages 21–30 (Mi mm4203)

Self-consistent calculation of the ground state of a hydrogen-like carbon atom in a graphene lattice

B. G. Freinkman

Keldysh Institute of Applied Mathematics of RAS

Abstract: With the discovery of graphene, the era of the development of fundamentally new materials began. Their unique properties already allow you to create many useful products in electronics, biomedicine and other high-tech industries. However, the study of graphene and its derivatives continues. The mechanism of the formation of the graphene lattice and the state parameters of its individual atoms are still not fully understood. The reason for this is the fact that graphene itself cannot be obtained without laying carbon atoms on a surface with certain properties. But in this case, the properties of graphene are substantially obscured by the properties of the surface itself. This work is devoted to the creation of a graphene model in the form of a lattice of hydrogen-like carbon atoms. In this case, we use a modification of the Brandt-Kitagawa approach with shielded ions that we proposed earlier. In the cold lattice approximation, this model assumes that the three valence atoms oriented along the bond lines belong to the ion shield. And only one valence electron determines the ground state of the lattice atom and the inhomogeneous angular distribution of its field.

Keywords: graphene lattice, hydrogen-like atom, ground state, self-consistent solution of the Schrodinger equation, inhomogeneous central field.

 Funding Agency Grant Number Russian Foundation for Basic Research 20-07-00790_a

DOI: https://doi.org/10.20948/mm-2020-08-02

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Revised: 16.04.2020
Accepted:21.05.2020

Citation: B. G. Freinkman, “Self-consistent calculation of the ground state of a hydrogen-like carbon atom in a graphene lattice”, Matem. Mod., 32:8 (2020), 21–30

Citation in format AMSBIB
\Bibitem{Fre20} \by B.~G.~Freinkman \paper Self-consistent calculation of the ground state of a hydrogen-like carbon atom in a graphene lattice \jour Matem. Mod. \yr 2020 \vol 32 \issue 8 \pages 21--30 \mathnet{http://mi.mathnet.ru/mm4203} \crossref{https://doi.org/10.20948/mm-2020-08-02}