Collision of protons with carbon atoms of a graphene surface in the presence of adsorbed potassium

Abstract

In this work we study the frontal collision of protons with the carbon atoms of a graphene surface with a low coverage of adsorbed potassium. It is aimed at the analysis of the effect of the adsorbates in both charge exchange and electron emission processes, when the binary collision occurs between the proton and a carbon atom of the surface. The frontal collision with the K adsorbate, already analyzed and discussed in a previous work, is compared with the frontal collision with different carbon neighbors. In the present work we studied the signals, due to the localized structures in the density matrix of the composed graphene plus potassium surface, that can be distinguished when the collision occurs either with the adsorbate, a nearby carbon atom, or a carbon atom that does not feel the presence of the adsorbate. The interacting system is described by the Anderson Hamiltonian which takes into account the electronic repulsion on the projectile site; the charge fractions, the energy distribution of electrons in the solid, and the electron emission after the collision are calculated by using the nonequilibrium Green-Keldysh functions formalism solved by the equation of motion method. In the binary collision with a carbon atom, the extended features of the band structure of graphene smooth the dependence of the projectile charge fractions on the incoming energy and notably decrease the negative ions formation. The localized structures of the density of matrix caused by the presence of the adsorbate are perceptible for scattered carbon atoms close to K. The intense emission of low energy electrons obtained in the case of the scattering by potassium is fundamentally associated with the very localized K-$4s$ empty band. This characteristic, although less marked, remain in the scattering by nearby carbon atoms, due to both the interaction with K along the projectile trajectory and the perturbed local density of states on the carbon atoms due to the adsorbate presence. In addition, the extended nature of the electronic structure of graphene allows for the emission of more energetic electrons.