Floquet optical selection rules in black phosphorus

Abstract: The optical selection rules endorsed by symmetry are crucial for understanding the optical properties of quantum materials and the associated ultrafast spectral phenomena. Herein, we introduce momentum-resolved Floquet optical selection rules using the group theory to elucidate the pump-probe photoemission spectral distributions of monolayer black phosphorus (BP), which are governed by the symmetries of both the material and the lasers. Using time-dependent density functional theory (TDDFT), we further investigate the dynamical evolution of Floquet(-Volkov) states in the photoemission spectra of monolayer BP, revealing their spectral weights at specific momenta for each sideband. These observations are comprehensively explained by the proposed Floquet optical selection rules. Our framework not only clarifies experimental photoemission spectra but also uncovers novel characteristics under different pump-probe configurations. Our results are expected to deepen the understanding of light-induced ultrafast spectra in BP and can be further extended to other Floquet systems.