Hydrogen ion scattering from alkali/graphene surface: Alkali core states effects

Abstract

We present a theoretical study of the frontal collision of protons with a graphene surface to which an alkali-adatom is added. Na and Cs adsorbates are studied in a low coverage limit. We analyze how the presence of adsorbates affects the charge exchange when the binary collision between the H+ protons and the adatoms or different carbon atoms close to the impurity occurs. The charge transfer process in the scattering of protons in the K and C atoms of a graphene surface to which a K adatom is added has already been analyzed and discussed in our previous works. We find that the inner states of the alkali atoms adsorbed on graphene introduce important differences in the charge transfer depending on their positions with respect to the valence band of graphene. For a better grasp of this, in this work we select Cs and Na as adatoms due to Cs has core levels that can resonate with the valence band of graphene, while Na does not. The interacting system is described by the Anderson Hamiltonian which takes into account the electronic repulsion at the projectile site; the ion charge fractions after the collision are calculated by using the non-equilibrium Green-Keldysh functions formalism. Also, we describe the adsorption of the alkali atom on the surface using the single impurity Anderson model and introduce the Green's functions required to calculate the adatom spectral density. In the scattering of H+ from Cs, the charge fractions as a function of the incident energy, behave similarly to the scattering from K. For the Na adatom, the dependence is different, showing a monotonous increase in the high energy regime. The results of this work allow us to infer the signals in the charge exchange, from the localized features of the density of states on the alkaline adsorbate during the scattering process, due to the peculiarities of the electronic band structure of graphene.