# Neutralization Dynamics of Slow Highly Charged Ions in 2D Materials
## 3 Discussion on Ion Interaction with 2D Materials
### Single Layer Graphene  
The charge exchange of highly charged ions  
\[\Delta Q=Q_{\text{in}}-\overline{Q}_{\text{exit}}=Q_{\text{in}}\left(1-\text{e }^{-t/\tau_{\text{in}}}\right) \tag{2}\]  
depends on the interaction time \(t\) and a time constant for neutralization \(\tau_{\text{in}}\). We could show that the neutralization time constant is in the range of 1-5 fs, depending on the incident charge state (\(\tau_{n}=\tau_{n}(Q_{\text{in}})\)) [2; 23]. At the same time, the ion energy loss \(\Delta E_{\text{kin}}\) depends quadratically on the incident charge state \(Q_{\text{in}}\) as well as on the charge exchange \(\Delta Q\). With the help of time-dependent density functional theory (TD-DFT) simulations [2], adapted for highly charged ion impact, a fast above-surface charge transfer is observed similar to the predictions of the COB-model. In addition, an energy loss, which scales quadratically with the incident charge state, was observed. From the simulations, an intuitive picture of charge state dependent energy loss of slow ions (above the surface) can be drawn. As soon as the ion extracts electrons from the graphene, a positive charge patch is formed. Transported electrons need to reverse their momentum vector to follow the ion, i.e., after extraction they need to turn around. Since the ion is further approaching the surface, captured electrons lag behind the ion forming a negatively charged wake (similar to the findings for swift ions close to the surface [55]). At this point, the unscreened ion charge (screening is anisotropic due to the wake) and the transiently formed charge patch lead to a retarding Coulomb force. The ion charge at this point is proportional to the incident value. The amount of positive charge of the charge patch will also be proportional to the ion incident charge state and thus the stopping force is proportional to \(Q_{\text{in}}^{2}\). After the ion passed the graphene layer, the TD-DFT simulations show an isotropic screening of the ion nuclear charge and thus no long-range Coulomb forces act on the ion after passage. Our measurements, and to some extent the simulations, show that ion stopping in the pre-equilibrium regime depends on the incident charge state as well as on the amount of charge exchange. Thus, there exists a close connection between ion stopping and the ion's neutralization dynamics. The simulations further predict a large in-plane current density of electrons moving towards the impact area and neutralizing the impact zone. As a result, pore formation is suppressed. Figure 7: (Color online) TEM image of SLG after 180 keV Xe\({}^{40+}\) irradiation. Some residual contamination can be observed on an otherwise intact graphene sheet. No single ion-induced defects can be observed. The inset shows a FFT of the image. The TD-DFT simulations [2] give nice explanations for the observed stopping force and describe the electron transport before the ion impacts on the graphene layer well. However, they cannot take atomic and inter-atomic deexcitation processes into account. The lack of deexcitation processes in the TD-DFT simulations leads to a simulated charge exchange, which is independent of the ion velocity. This is in contradiction to experimental data, e.g., in Figure 6c. Energy is transferred to the target by ion stopping (few keV, see above) as well as ion neutralization and deexcitation. The latter is the potential energy deposition (few 10 keV) and may even be greater than the energy deposition by stopping. The formation of a hollow atom in front of the material's surface, as it is described by the COB-model, is dominated by resonant charge transfer, i.e., the potential energy remains stored in the ion as the total excitation potential of the hollow atom. It is the ion's deexcitation which releases the potential energy. Deexcitation in hollow atoms is, to a major extent, driven by non-radiative Auger-type processes. Radiative processes contribute only to a minor extent, because of small transition rates [56; 57].