Time-dependent density-functional theory simulation of electron wave-packet scattering with nanoflakes

Low-energy electron scattering with nanoflakes is investigated using a time-dependent density functional theory (TDDFT) simulation in real time and real space. By representing the incident electron as a finite-sized wave packet, we obtain diffraction patterns that show not only the regular features of conventional low-energy electron diffraction (LEED) for periodic structures but also special features resulting from the local atomic inhomogeneity. We have also found a signature of $\pi$ plasmon excitation upon electron impact on a graphene flake. The present study shows the remarkable potential of TDDFT for simulating the electron scattering process, which is important for clarifying the local and periodic atomic geometries as well as the electronic excitations in nanostructures.

Figure 1

Snapshots of the electron densities of the target WP before and after the scattering. The WP is incident to the target from a distance $D$, at which an observation plane for the simulation of LEED patterns is also placed to capture the diffracted electrons.

Figure 2

Target flakes (left) and the simulated diffraction patterns (right). (a) A coronene (${\mathrm{C}}_{24}$${\mathrm{H}}_{12}$), (b) a double-layer coronene, and (c) a circumcoronene (${\mathrm{C}}_{54}$${\mathrm{H}}_{18}$). The color scales are the same in the right panels. (d) The relative intensities of the outer spots ($I_2$) to the inner spots ($I_1$) for (a) and (b).

Figure 3

Target flakes (left) and the simulated diffraction patterns (right). (a) A circumcoronene with a vacancy and (b) a BN flake (${\mathrm{B}}_{12}$${\mathrm{N}}_{12}$${\mathrm{H}}_{12}$). B and N atoms correspond to the largest and medium-sized dots, respectively. All color scales for the diffraction patterns in the right panel are the same as in Fig. 2.

Figure 4

Impact-point dependent diffraction patterns. (a) A hexagon in the circumcoronene. The three impact points are indicated by O, P, and Q. The patterns for the impact points P and Q are given respectively in (b) and (c), while that for O is given in Fig. 2.

Figure 5

(a) Dipole excitation in a circumcoronene caused by an electron WP with a kinetic energy of 200 eV and (b) optical absorption cross section in a circumcoronene caused by an external optical field in the form of a $\delta$ function in the linear response regime. The excitation energies of $\pi$ and $\pi +\sigma$ plasmons observed in the EELS experiment [44] are indicated by arrows.