  We theoretically investigate the orientation dependence of high-harmonic
generation (HHG) in monolayer transition metal dichalcogenides (TMDCs). We find
that, unlike conventional solid-state and atomic layered materials such as
graphene, both parallel and perpendicular emissions with respect to the
incident electric field exist in TMDCs. Interestingly, the parallel
(perpendicular) emissions principally contain only odd-(even-) order harmonics.
Both harmonics show the same periodicity in the crystallographic orientations
but opposite phases. These peculiar behaviors can be understood on the basis of
the dipole moments in TMDCs, which reflect the symmetries of both atomic
orbitals and lattice structures. Our findings are qualitatively consistent with
recent experi- mental results and provide a possibility for high-harmonic
spectroscopy of solid-state materials.
