High-harmonic generation from few-layer hexagonal boron nitride: Evolution from monolayer to bulk response

Two-dimensional materials offer a versatile platform to study high-harmonic generation (HHG), encompassing as limiting cases bulklike and atomiclike harmonic generation [Tancogne-Dejean and Rubio, Sei. Adv. 4, eaao52(7 (7018)]. Understanding the high-harmonic response of few-layer semiconducting systems is important and might open up possible technological applications. Using extensive first-principles calculations within a time-dependent density functional theory framework, we show how the in-plane and out-of-plane nonlinear nonperturbative responses of two-dimensional materials evolve from the monolayer to the bulk. We illustrate this phenomenon for the case of multilayer hexagonal BN layered systems. Whereas the in-plane HHG is found not to be strongly altered by the stacking of the layers, we found that the out-of-plane response is strongly affected by the number of layers considered. This is explained by the interplay between the induced electric field, resulting from the electron-electron interaction, and the interlayer delocalization of the wave functions contributing most to the HHG signal. The gliding of a bilayer is also found to affect the high-harmonic emission. Our results will have important ramifications for the experimental study of monolayer and few-layer two-dimensional materials beyond the case of hexagonal BN studied here as the results we found are generic and applicable to all two-dimensional semiconducting multilayer systems.