Hydrogen ion scattering from a potassium impurity adsorbed on graphene

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 $\mathrm{K}\text{−}3s$ 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.

Figure 1

Total density of states on the adatom (K). The partial contributions from the valence $4s$ and inner $3p$ K orbitals are indicated. The inset shows a close up view of the small $4s$ contributions that cannot be appreciated in the main figure.

Figure 2

(a) C neighbors of the K adatom indicated by the crossed circle. (b) Graphene partial $s$ density of states on C atoms at different distances from the potassium; the line color indicates the corresponding C atom with the same color in (a). (c) and (d) show, respectively, a larger version of the changes in the regions between 1 and 2 eV, and between −15 and −20 eV. As reference, the local and partial $s$ density of states for the clean graphene surface is also shown (black dashed-dotted-dotted line).

Figure 3

The same as in Fig. 2 for the graphene partial $p_z$ density of states on C atoms at different distances from the potassium.

Figure 4

Scattering geometry. The zero distance is at the K atom, the six C atoms included in the calculation are highlighted.

Figure 5

The ionization and affinity energy levels of H as a function of the normal distance $z$ to the potassium atom. The striped area corresponds to the graphene surface LDOS and the peaked structure corresponds to the projected LDOS on the K adatom. The position of the 3s core state of potassium is also indicated (dashed line).

Figure 6

Coupling terms $V_{\alpha m,a}^{}\left(z\right)$ as a function of the normal distance to the surface $z$ for H / K and H / C dimeric systems (for H/C are multiplied by 20). The zero of distances is located in the K atom position.

Figure 7

The energy level and its width (see the text) shown as error bars: within an independent electron model (gray line) and by considering electronic correlation (black line). (a) Ionization level, (b) affinity level. The shadowed area corresponds to the K LDOS (the Fermi energy is set on zero).

Figure 8

(a) Neutralization probability as a function of the incoming proton energy (black full squares), hole occupation in region 1 (red empty circles), hole occupation in region 2 (blue empty triangles), hole occupation in region 3 (orange empty down triangles), electron occupation in region 4 (green full diamonds); (b) the ionization level and its width as a function of distance to the K adatom, the projected density of states on K, and the shadowed areas indicate the different regions 1, 2, 3, and 4; (c) the distance evolution (negative values of $z$ indicate the incoming path) of the neutralization probability for incoming energies 1000 eV (blue empty squares) and 2000 eV (red empty circles).

Figure 9

(a) Negative ion formation probability as a function of the incoming neutral atom energy (black full squares), hole occupation in region 1 (red empty circles), hole occupation in region 2 (blue empty up triangles), hole occupation in region 3 (orange empty down triangles), electron occupation in region 4 (green full diamonds); (b) the affinity level and its width as a function of distance to the K adatom, the projected density of states on K, and shadowed areas indicate the different regions 1, 2, 3, and 4; (c) the distance evolution of the negative ionization probability for incoming energies 1000 eV (blue empty squares) and 2000 eV (red empty circles).

Figure 10

Ion fractions as a function of the incoming energy: $P^0$ (full circles), $P^{-}$ (full squares), and $P^{+}$ (full triangles).

Figure 11

Distance evolution of (a) the neutral ion fraction and (b) the negative ion fraction, for incoming energies 1000 eV (red dashed-dotted line) and 2000 eV (blue dashed line).

Figure 12

(a) Neutral ion fraction and (b) negative ion fraction as a function of incoming energy. The calculation including the inner and valence states of K adatom (black full squares) and the calculation considering only the $4s$-band states (blue full down triangles). Full circles (red) show the negligible contribution of the carbon atoms because they are very far from the projectile.

Figure 13

Neutral (black lines) and negative (gray lines) ion fractions as a function of distance in the case of considering only the $4s$-band states of the adsorbed potassium, for incoming energies: 1000 eV (short-dashed-dotted line) and 2000 eV (solid line).

Figure 14

Ion fractions as a function of the projectile incoming energy calculated by considering (full symbols) and not considering (empty symbols) correlation effects. The squares correspond to negative $\left({\mathrm{\Gamma }}^{-}\right)$, and circles to neutral $\left({\mathrm{\Gamma }}^0\right)$ fractions.