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

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.

💡 Research Summary

This paper presents a comprehensive theoretical investigation into the three-dimensional (3D) real-space electron dynamics of graphene under intense laser fields, employing time-dependent density functional theory (TDDFT). The study serves both as a rigorous verification of prior model-based predictions and as a discovery platform for new physical phenomena beyond lower-dimensional approximations.

The research successfully reproduces a key phenomenon predicted by earlier tight-binding combined with semiconductor Bloch equations (TB-SBE): the reversal of the light-induced residual current direction with increasing laser field strength. This reversal originates not from a uniform cessation of current but from the spatial cancellation of two oppositely directed microscopic current channels within the graphene unit cell—one flowing along the hexagonal ring of carbon bonds and the other flowing through the center of the hexagon. By decomposing contributions from individual electronic orbitals, the TDDFT results validate the two-level system approximation for weaker fields near the Dirac cone. However, they also highlight its limitations, showing that the first-principles TDDFT approach yields better agreement with experimental residual current measurements, especially in the extremely strong field regime (above ~3 V/nm). This is attributed to TDDFT’s inherent ability to capture complex multi-band effects and tunneling excitations far from the Dirac point that become significant at high intensities.

The most significant and novel finding of this work is the revelation of the full 3D spatial structure of the laser-induced atomic-scale currents. While the 2D projection of the current onto the graphene plane confirms the spatially separated, counter-propagating ring currents, the 3D analysis uncovers a crucial out-of-plane dimension. The calculations demonstrate that the current density is not strictly confined to the graphene basal plane. Instead, the two opposing current channels exhibit a pronounced vertical separation: the current along the hexagonal ring is concentrated slightly above the atomic plane, while the backward current through the hexagon center is concentrated slightly below it. This indicates that the light-driven “ring current” is not a simple 2D circulation within the plane but rather forms a rotating 3D circulation loop, akin to a pair of vertically offset current rings.

Methodologically, the study uses an orthogonal unit cell with four carbon atoms and a substantial vacuum layer, computed with the SALMON code. It first establishes the credibility of the approach by accurately reproducing graphene’s linear optical properties, such as its characteristic conductivity spectrum and Dirac cone band structure. The nonlinear dynamics are then induced by few-cycle, linearly polarized laser pulses. Analysis in reciprocal space shows the evolution of asymmetric carrier distribution from multiphoton resonance to dominant tunneling excitation as the field intensifies.

In conclusion, this work underscores the power of first-principles, real-space TDDFT simulations for uncovering intricate details of ultrafast electron dynamics in solids. It confirms established models in certain regimes while fundamentally advancing our understanding by revealing the genuine 3D nature of optoelectronic responses in an atomically thin material like graphene. This insight into the depth profile of photocurrents opens new perspectives for designing and interpreting experiments related to light-wave electronics and valleytronics in 2D materials.