Transition dipole moment structure revealed by high harmonic generation spectroscopy in thin layer black phosphorus

Abstract

High harmonic generation (HHG), which emits radiations with integer multiples of incident laser photon energy, is the most essential nonlinear optical phenomena for attosecond science in the atom and molecular systems. The recent development of intense infrared laser source enables us to induce HHG even in solid system without the damage to samples [1] . HHG in solids shows unique characteristics different from the atomic system, such as anisotropic response in HHG efficiency and polarization selection rule, and these are linked to microscopic electronic structure such as band structure, Berry curvature, and valence electron density [2] - [4] . HHG and the related phenomena have a great potential to probe hidden physical properties in solid. However, the HHG mechanism is still under debate, and the correspondence between HHG properties and microscopic electronic structure is still unclear. In this aspect, black phosphorus (BP) is a fascinating system to investigate HHG properties in solids. The electronic system in BP can be well regarded as a two-band system from infrared to visible range. Also, there is a strong in-plane anisotropy in BP. Effective mass along the armchair(AC) direction is much lighter than that along the zigzag(ZZ) direction for both electrons and holes, and the interband transition at band minimum (Z point) is forbidden along ZZ direction [5] . Such a simple two-band system with strong anisotropy can be used to distinguish HHG mechanism and clarify the connection between HHG and microscopic electronic properties.