# Neutralization Dynamics of Slow Highly Charged Ions in 2D Materials
## 1 Introduction  
Interaction studies of slow highly charged ions (HCI) with single atoms, molecules and solids are an active field of basic and applied physics research [1; 2; 3; 4; 5]. Many experimental and theoretical studies were performed to understand the neutralization process above the surface and surface modification due to potential energy deposition in the topmost atomic layers [6; 7; 8; 9; 10]. While the charge transfer above a surface is well described by the classical-over-barrier (COB) model, the mechanisms at work inside the solid after ion impact, i.e., electron capture, deexcitation processes, and stopping, are still not fully understood. The challenge arises from the fact that ions travelling in a 3D solid will rapidly reach their equilibrium charge state, which is independent of the original charge state and just determined by the ion velocity, limiting the access to the pre-equilibrium regime of the interaction [11; 12; 13; 14]. To gain experimental access to the pre-equilibrium regime, 2D materials come into play as they provide a solid target with only atomic thickness. They allow an experimental observation of phenomena during the pre-equilibrium time in simple beam-foil experiments. Open fundamental questions such as the role which charge state and charge exchange play in slow ion stopping, can now be addressed with the availability of these materials. It may, e.g., be questioned, whether the ion interaction with a 2D solid can be described by extrapolating models derived for 3D solids (thick material) to zero thickness or if qualitatively new phenomena emerge. Additionally, the technological use of ion beams in tailoring optical, electronic, and structural properties of 2D materials for applications such as controlled production of nano-sieves needed in DNA sequencing [15] or adjusting the p- and n-type doping for solar cell applications [16; 17] is a major motivation of the work. The deliberate production of defects, the direct implantation of ions, and the perforation of the material will determine the 2D material's mechanical, optical, and electronic properties. Here, we review recent work on HCI irradiation of 2D materials, which is a young subfield of ion-solid  
interaction. As there exists only a limited body of research and many groups are currently joining the field, we focus mainly on our own work over the last five years [2; 18; 19; 20; 21; 22; 23; 24] with the aim to give an overview for newcomers. By using HCIs, we benefit from a unique property of (heavy) ions: the available potential energy resulting from the charge state. By successive removal of electrons from the atomic shells of an ion, the total ionization potential of a certain charge state is stored as the potential energy in the ion. Figure 1 shows the potential energy for Ar and Xe ions as a function of the charge state. It can reach up to several 10 keV for Xe charge states above 30. The potential energy is released as soon as the ion neutralizes and deexcites in the vicinity of a surface. It is generally believed that, upon approach towards a solid surface, a HCI starts to capture electrons above the Coulomb barrier between the surface and the ion [6; 25]. Figure 2 shows the electrostatic potential in front of a metallic surface according to the COB-model [6] for a Xe\({}^{30+}\) ion in close proximity of 5 A to the atomic plane of the surface along the ion-surface axis. The potential barrier between the surface and the ion is significantly lowered allowing resonant electron transport to the ion. Electrons, which were captured resonantly, occupy states in the ion with principal quantum numbers of \(n>30\). Resonant charge capture is typically fast enough (<1 fs) for almost complete neutralization above the surface [26]. The neutralized atom, however, is left with a plethora of empty inner shells. It is referred to as a _hollow atom_[26]. Even though the COB-model works well, both as an instructive model and for quantitative comparison to grazing scattering experiments [27; 28], it fails to work within a solid.