Observing quantum-path interference and Van Hove singularity in polarization-resolved high-harmonic spectroscopy

High-harmonic spectra in solids driven by linearly polarized laser pulses contain diverse polarization dependence and fine modulation in the harmonic yields. In this work, we attribute the direction-dependent features of harmonic yields to the collective roles of tunneling rate, quantum-path interference, and joint density of state (JDOS). In addition, we distinguish the dominant contribution between quantum-path interference and the Van Hove singularity of JDOS, and demonstrate that the emergence of spectral enhancement in the vicinity of cutoff frequency is determined by the Van Hove singularity of JDOS. Polarization-resolved high-harmonic spectra are a promising spectroscopic tool to probe the electronic structure and dynamics in solids and thus open a door to measure Van Hove singularities and the energy band with high-resolution crystal momentum.