Hydrogen ion scattering from a potassium impurity adsorbed on graphene

Abstract

In this work we study the charge exchange process in the scattering of protons by potassium atoms adsorbed on a graphene surface in a low coverage limit. Both, the projected density of states on the alkaline atom site and the final charge states of the hydrogen projectile are calculated by considering the electronic Coulomb repulsion in the $s$-valence orbital. The inner $3p$ and $3s$ states of potassium are included and the local perturbations of the density matrix on the surrounding C atoms are also considered. The interacting systems are described by an Anderson Hamiltonian whose terms are calculated from the chemical properties of the atoms and the extended features of the graphene surface. The positive and negative ion fractions of hydrogen in the collision process are obtained from Keldysh-Green functions, which are calculated by employing the equation of motion method closed up to a second order in the atom-surface coupling term. It is found that the carbon atoms have no possibility of a direct charge exchange process in a frontal collision of the proton with the K adatom, and that the K-$3p$ band, broadened by the interaction with the graphene surface, provides an important source of electrons for the negative ionization of hydrogen, which is also promoted by the presence of a $\mathrm{K}\text{\ensuremath{-}}3s$ core state. The narrow $4s$ and $3p$ bands of the adsorbed potassium lead to an oscillatory dependence with the projectile incoming energy, of the probability for the three correlated charge states of hydrogen.