Visualization of two-dimensional transition dipole moment texture in momentum space using high-harmonic generation spectroscopy

Highly nonlinear optical phenomena can provide access to properties of electronic systems which are otherwise difficult through conventional linear spectroscopies. In particular, high-harmonic generation (HHG) in crystalline solids is strikingly different from that atomic gases, and it enables us such as the band structure, Berry curvature, valence electron density. Here, we show polarization-resolved HHG measurements with band-gap resonant excitation be used probe transition dipole moment (TDM) texture momentum space two-dimensional semiconductors. TDM directly related internal structure system governs properties. We study black phosphorus, offers a simple two-band system. observed unique crystal-orientation dependence yields polarizations. Resonant edge reconstruct interatomic bonding structure. Our results demonstrate potential spectroscopy for probing wave functions solids.