  We report a coherent layer-by-layer high-order harmonic generation (HHG)
build-up in artificially stacked transition metal dichalcogenides (TMDC)
crystals in their various stacking configurations. In the experiments,
millimeter-sized single crystalline monolayers are synthesized using the gold
foil-exfoliation method, followed by artificially stacking on a transparent
substrate. High-order harmonics up to the 19th order are generated by the
interaction with an ultrafast mid-infrared (MIR) driving laser. We find that
the generation is sensitive to the number of layers and their relative
orientation. For AAAA stacking configuration, both odd- and even-orders exhibit
a quadratic increase in intensity as a function of the number of layers, which
is a signature of constructive interference of high-harmonic emission from
successive layers. Particularly, we observe some deviations from this scaling
at photon energies above the bandgap, which is explained by self-absorption
effects. For AB and ABAB stacking, even-order harmonics remain below the
detection level, consistent with the presence of inversion symmetry. Our study
confirms the capability of producing non-perturbative high-order harmonics from
stacked layered materials subjected to intense MIR fields without damaging
samples. It has implications for optimizing solid-state HHG sources at the
nano-scale and developing high-harmonics as an ultrafast probe of artificially
stacked layered materials. Because the HHG process is a strong-field driven
process, it has the potential to probe high-momentum and energy states in the
bandstructure combined with atomic-scale sensitivity in real space, making it
an attractive probe of novel material structures such as the Moir\'e pattern.
