# Neutralization Dynamics of Slow Highly Charged Ions in 2D Materials
## 3 Discussion on Ion Interaction with 2D Materials
### Single Layer Graphene
To identify which Auger-type processes (atomic or intra-atomic) are dominating, we need to reconsider the measured neutralization time constants of 1-5 fs and compare those with the typical Auger deexcitation lifetimes. Atomic deexcitation, especially in the outer shells \(n\gg 1\), proceed on the 1-100 fs time scale [58]. Hence, they are active mostly when the ion has passed the graphene sheet already. Consequently, the deexciting hollow atom emits (energetic) Auger electrons and charges up again. Further supply of electrons to the ion is prohibited, because it is not in contact with the target anymore. Our observed low exit charge states, and even neutral projectiles at \(v<10^{5}\) m/s, are in conflict with this description. After a hollow atom has formed above the surface, a deexcitation process must be active, which suppresses electron loss by auto-ionization. It can only appear in close contact with a large atomic cluster or a solid surface by energy release to the target atoms [59]. Related processes are termed electron transfer mediated decay (ETMD) and interatomic coulombic decay (ICD) [60]. ETMD involves non-resonant target electron transfer directly into core-levels of the ion and energy uptake by another target electron. It is ineffective in our case, because of a small wave function overlap of the target electron with the core orbital of a highly charged ion (see Figure 2). ICD, however, is an energy release mechanism without electron transfer. Outer projectile electrons, in our case previously (COB) transported electrons, transfer their excitation energy to valence electrons of the target, which also have a large spatial extent. The energy transfer works via electron-electron interaction. In this way, outer electrons in a hollow atom can deexcite by excitation (and ionization) of target electrons and without ionization of projectile electrons. ICD has a lifetime or rate, which depends strongly on the interatomic distance of the projectile and the target as well as on the target size, i.e., number of nearest neighbours [61; 62; 63]. The closer the projectile and the target get, or the more target atoms donate electrons to the process, the stronger the electron-electron interaction and the faster ICD becomes. The lifetime of ICD is in the range of 1-5 fs, i.e., well in the range of our ion-SLG interaction time [62]. The ratio of ICD lifetime and HCI interaction time defines a competition between survival of outer projectile electrons (later auto-ionized) and hollow atom quenching (without recharging). Thus, it defines the amount of potential energy, which can be transferred to a 2D target and it explains our observed velocity (and time) dependence of charge exchange. In summary, HCI neutralization proceeds as a two-step process [23] depicted in Figure 8. At first, the HCI extracts electrons classically over the Coulomb barrier between ion and surface. Electrons are transferred resonantly, i.e., no potential energy is transferred or released. The electrons are weakly bound to the ion in orbitals with high quantum numbers \(n>20\) and large spatial extent (\(\leq\)10 A). The extraction of the electrons forms a positive charge patch at the surface. The reversal of the direction of motion of the transferred electrons leads to a distortion of the bound electron density. A Coulomb force acts on the ion and contributes to its stopping. As soon as the ion is close enough to the surface atoms, ICD sets in and leads to a fast deexcitation of the projectile's outer electrons by excitation of target electrons. The target surface is further positively charged by electron ionization (observable in experiment as a high yield of slow electrons) and atomic bonds in the impact area are weakened by excitation of target electrons from the valence band into the conduction band (binding to anti-binding states). If the ion is initially slow enough (\(v\lesssim\Gamma d\), if \(\Gamma\gtrsim 0.04\) a.u.