In the framework of time-dependent density-functional theory, we obtain high-order harmonics of photon energies up to $10U_p$ from bilayer crystals with an interlayer spacing $d=70\AA$. At grazing incidence, a clear double-plateau structure is observed in the harmonic spectrum. The photon energy of the second plateau far beyond atomiclike harmonics can be well explained by the inclusion of backscattering of ionized electrons. Ab initio simulations reveal that the cutoff of the second plateau is continuously extended with an increasing $d$. Our classical calculations predict that the maximum electronic kinetic energy is linearly dependent on $d$ over a wide range. Moreover, the harmonic yield in the second plateau is significantly enhanced by increases in the wavelength of the driving laser. Owing to the confined spreading of the electronic wave packet, a beneficial wavelength scaling of ${\lambda }^{2.85}$ is obtained. This study therefore establishes an efficient way of producing high-energy photon source based on layered nanostructures.

• Received 1 June 2020
• Accepted 30 November 2020

DOI:https://doi.org/10.1103/PhysRevB.102.241407