Three-dimensional real-space electron dynamics in graphene driven by strong laser fields

TL;DR

The paper addresses real-space, three-dimensional electron dynamics in graphene under strong laser fields and the mechanism behind current reversal. It uses real-time TDDFT to compute the time-dependent current density $\mathbf{J}(\mathbf{r},t)$ and the residual current $I(t)$, decomposing contributions by orbital character and benchmarking against two-level SBE models and experimental data. Key findings include field-induced current reversal at $F \sim 2$ and $3.56\,\mathrm{V/nm}$, dominance of the $8^{th}$ and $9^{th}$ orbitals near the Dirac cone at moderate fields, and the emergence of higher-band contributions at strong fields; importantly, the real-space current forms a rotating 3D loop located slightly above and below the graphene plane, not confined to it. This work links reciprocal-space intuition with a three-dimensional real-space picture, providing ab initio insights for ultrafast lightwave electronics.

Abstract

We theoretically investigate the three-dimensional (3D) electron dynamics of graphene in real space under strong laser fields using time-dependent density functional theory (TDDFT). We successfully reproduce the reversal of current direction originating from the cancellation of two oppositely directed residual currents, as previously predicted by Morimoto et al. [Y. Morimoto et al., New J. Phys. 24, 033051 (2022)]. By distinguishing contributions from individual orbitals, our results validate the two-level system approximation and also emphasize that the first-principles approach agrees better with experimental results for light-driven residual current, especially in extremely strong fields. Furthermore, our 3D model reveals that the real-space atomic-scale current induced by strong laser fields is concentrated slightly above and below the graphene basal plane, rather than strictly within it. The two oppositely directed currents exhibit a pronounced height separation in the out-of-plane direction, indicating that the ring current is not confined to the graphene plane but forms a rotating 3D circulation loop which is absent in the reduced-dimensional model.

Figures (9)

• Figure 1: Band structure of each orbital along high symmetry $\Gamma-P-X-W$ direction, for each orbital. Open circles represent the DFT results while the solid line indicates the tight-binding results.
• Figure 2: (a) Top view and (b) side view of normalized charge density in real space. A and B show position at the midpoint of a C–C bond and at the center of the hexagonal structure, respectively, projected onto the $xy$ plane. C and D correspond to the midpoint of a C–C bond oriented at 0$^\circ$ and 60$^\circ$ with respect to the x-axis, respectively. Black circles indicate carbon nuclei. All densities are normalized.
• Figure 3: Linear response of graphene computed with TDDFT. The green line shows the real part of conductivity. Black and red dots are results from DFT calculations rani2014dftsedelnikova2011ab. The horizontal pink dashed line indicates the zero-frequency conductivity ($\sim$0.25 a.u.). The orange and purple vertical lines mark the two peak positions, corresponding to the $\pi\to\pi^*$ and $\sigma\to\sigma^*$ transitions, respectively.
• Figure 4: The excited population $P(k_x,k_y)$ on the reciprocal space after the laser fields. (a-h) Population near Dirac cone on the lowest conduction orbital (9th orbital) with contour lines on times of photon energy under the peak field amplitudes from 0.5 V/nm to 4 V/nm. (i) Normalized density of states for the excited population on conduction band. (j) excited carrier distribution asymmetry $\mathcal{A}(k_{x_0})$ normalized to its maximum value on 4 V/nm as a function of $k_x$. Positive (red) and negative (blue) background shadings indicate the sign of the asymmetry.
• Figure 5: Total residual current vs. peak field amplitude $F$. Green solid line: our TDDFT results (this work), orange dashed: calculated results by Morimoto $\textit{et al.}$morimoto2022atomic, blue circles: experimental data from Higuchi $\textit{et al.}$higuchi2017light ($\leq$ 3 V/nm) extended by Weitz $\textit{et al.}$weitz2024strong. The plots are normalized by the maximum of the residual current, respectively.