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

Abstract

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