Optical Nonlinearities in Hexagonal and Triangular Graphene Quantum Dots

Graphene quantum dots (GQDs), the graphene nanoparticles of a few nanometers excited by an ultrafast optical pulse of a few femtoseconds, exhibit several optical nonlinearities, including residual population and high harmonic generation (HHG). By introducing dephasing, we addressed nonlinearity, namely HHG in GQDs placed in a short linearly polarized optical pulse. At short finite dephasing times, the ultrafast electron dynamics show significant irreversibility with a large residual population of the excited quantum dot levels. When dephasing time increases, intensities correspond to a low-frequency boost, while the cutoff energy decreases regarding the high harmonic spectra. The cutoff energy's dependence on the optical pulse's amplitude is also sensitive to the frequency of the pulse. This dependence in hexagonal GQDs is almost linear when the optical pulse frequency is much less than the quantum dot band gap. However, when the pulse frequency is comparable to the band gap, the cutoff energy shows saturation behavior at a large field amplitude, >0.4 V/Å. In triangular graphene quantum dots with zigzag edges, the intensities of high harmonics show a strong dependence on the initial electron population of the edge states of the quantum dot. If a zigzag triangular quantum dot possesses an even number of edge states, then even high harmonics are strongly suppressed when half of the edge states of the quantum dots are populated before the pulse. For any other populations of the edge states, the odd and even harmonics are of comparable intensities.