  We demonstrated nonperturbative high harmonics induced by intense
mid-infrared light up to 18th order that well exceed the material bandgap in
monolayer transition metal dichalcogenides. The intensities of the even-order
high-harmonic radiation did not monotonically decrease as the harmonic order
increased. By comparing the high harmonic spectra with the optical absorption
spectra, we found that the enhancement in the even-order high harmonics could
be attributed to the resonance to the band nesting energy. The symmetry
analysis shows that the valley polarization and anisotropic band structure lead
to polarization of the high-harmonic radiation under excitation with the
polarization along the zigzag direction. We also examined the possible
recombination pathways of electrons and holes by calculating their dynamics in
real and momentum spaces based on three-step model in solids. It revealed that,
by considering the electrons and holes generated at neighboring lattice sites,
the electron-hole polarization driven to the band nesting region should
contribute to the high harmonic radiation. Our findings open the way for
attosecond science with monolayer materials having widely tunable electronic
structures.
