Electronic correlation effects in the response of graphene and MoS2 monolayers to the impact of highly-charged ions

TL;DR

This work analyzes how electronic correlations affect the ultrafast response of graphene and MoS$_2$ monolayers to the impact of highly-charged ions. Employing nonequilibrium Green functions in the time-linear HF-GKBA within a G1--G2 framework and a time-local embedding scheme, the authors capture correlation effects alongside resonant charge transfer to the ion. They find that correlations minimally influence graphene but significantly modify MoS$_2$ dynamics, including charge transfer, doublon formation, and the induced electrostatic potential that governs secondary-electron emission, thereby refining the understanding of SEE differences between the two materials. The results underscore the importance of many-body effects in semiconducting 2D materials and point to future improvements via GW, expanded band structure, and larger systems to connect with macroscopic experiments.

Abstract

The interaction of highly-charged ions with monolayers of graphene and MoS2 is theoretically investigated based on nonequilibrium Green Functions (NEGF). In a recent paper [Niggas et al., Phys. Rev. Lett. 129, 086802 (2022)] dramatic differences in the response of the two materials to an impacting slow ion were reported. Here, this analysis is extended, focusing on the effect of electron-electron correlations in the monolayer on the electronic response to the ion. We apply the recently developed time-linear G1-G2 scheme [Schluenzen et al., Phys. Rev. Lett. 124, 076601 (2020)] combined with an embedding approach [Balzer et al., Phys. Rev. B 107, 155141 (2023)]. We demonstrate that, while electronic correlations have a minor effect in graphene, they significantly influence the electron dynamics in the case of MoS2. Our key results are the ultrafast dynamics of the charge density and induced electrostatic potential in the vicinity of the impact point of the ion.

Figures (11)

• Figure 1: a) Finite honeycomb clusters with a number of $N_s$ sites, b) corresponding DOS compared to the DOS of the infinite lattice (tight binding).
• Figure 2: Visualization of the coupling scheme between the honeycomb sites (black dots) and the HCI (purple star). Depending on the initial charge $Z_0$ of the ion, an integer number of $Z_0/8$ sites of the cluster are coupled (purple squares). The spatial layout is chosen such that the coupling is as symmetric as possible.
• Figure 3: Total charge transfer as a function of the inverse ion velocity for different charge states. a) SLG: comparison between NEGF balzer_prb_23 and the present time-local embedding scheme, both in HF approximation, as well as experimental data gruber_ultrafast_2016. b) Comparison between the present simulations for SLG and MoS$_2$, compared to experimental data for MoS$_2$schwestka_charge_2020.
• Figure 4: Average charge density on the different rings around the ion impact point, for a) MoS$_2$ comparing HF and SOA self-energies; b) comparing SLG and MoS$_2$ in SOA. The inset depicts the spatial structure of the cluster with nearest-neighbor connections. The brightness of the colors decreases outward. The dotted vertical line indicates the time for which the induced potential is shown in Figs. \ref{['fig:electrostatic_potential_combined']} and \ref{['fig:potential-3d']}.
• Figure 5: Different energy profiles over the course of the simulation of a $N_{\mathrm{s}}=150$ MoS$_2$ cluster, interacting with a Xe$^{+32}$ ion with a kinetic energy of $E_{\mathrm{ion}}=113\,\text{keV}$. Solid lines represent the results of a HF simulation while dotted lines represent the results of a SOA simulation. The different energy forms are kinetic energy $E_{\mathrm{kin}}$ (black), HF energy $E_{\mathrm{HF}}$ (purple) and correlation energy $E_{\mathrm{corr}}$ (blue).