Stopping dynamics of ions passing through correlated honeycomb clusters

Abstract

A combined nonequilibrium Green functions-Ehrenfest dynamics approach is developed that allows for a time-dependent study of the energy loss of a charged particle penetrating a strongly correlated system at zero and finite temperature. Numerical results are presented for finite inhomogeneous two-dimensional Fermi-Hubbard models, where the many-electron dynamics in the target are treated fully quantum mechanically and the motion of the projectile is treated classically. The simulations are based on the solution of the two-time Dyson (Keldysh-Kadanoff-Baym) equations using the second-order Born, third-order and T-matrix approximations of the self-energy. As application, we consider protons and helium nuclei with a kinetic energy between 1 and 500 keV/u passing through planar fragments of the two-dimensional honeycomb lattice and, in particular, examine the influence of electron-electron correlations on the energy exchange between projectile and electron system. We investigate the time dependence of the projectile's kinetic energy (stopping power), the electron density, the double occupancy and the photoemission spectrum. Finally, we show that, for a suitable choice of the Hubbard model parameters, the results for the stopping power are in fair agreement with ab-initio simulations for particle irradiation of single-layer graphene.Comment: 13 pages, 12 figure

Processing and Characterization of Composites Curing by Microwave Irradiation

“…On the other hand, the result for void content for the process via thermal curing is compatible with the expected manual laminating values. [4][5][6][7][8][9][10][11][12]…”

Time‐dependent simulation of ion stopping: Charge transfer and electronic excitations

“…On the other hand, looking at horizontal cuts provides the time dependence of the proton energy: before the impact (negative z P ) the proton gains energy because it is attracted by the electrons of the cluster, whereas after the impact the proton loses energy to the electrons (more than it had gained before), see Figure 4) on a 54-site honeycomb cluster at correlation strength U = 4 J for different initial kinetic energies in the range 10 −1 keV/u < E P kin,0 < 10 3 keV/u, indicated on the y-axis. A general discussion of this behavior has been given in Balzer et al [13] Here we provide more details of the physics including a breakup of the energy gain of the electrons into different contributions: potential energy in the field of the projectile, kinetic energy, mean-field energy, and correlation energy. Since the projectile velocity is almost constant, the height is a measure of time.…”

“…Below we present numerical results of the KBE coupled to the semiclassical projectile dynamics, as introduced in Balzer et al [13] We consider two honeycomb clusters that are described by the Hubbard model (9) containing L = 24 and L = 54 sites, respectively, see Figure 4 for a sketch of the former. We start by giving an overview of the general dynamical behavior of correlated 2D systems during the impact of a charged particle.…”

“…To reach sufficiently long simulation times, in this case, we do not perform an adiabatic switching on of the interaction U but start from the Hartree ground state, for the inclusion of a correlated initial state, see Semkat et al [78,79] . In this case the proton impact should occur only after the initial transient ∑ ⟨n (t −∞ )⟩ = 0.25 to some smaller value (for details see Balzer et al [13] ).…”

“…Extending the work of Balzer et al, [13] we consider in the following two different initial positions of the proton: the points S (cluster center, blue) and C (centroid point, red) as sketched in Figure 4. Figure 4a and b shows the energy loss in a broad range of proton energies between 0.05 and 25 keV/u for three different values of the interaction strength U/J ≤ 4.…”