Magic high-order harmonics from a quasi-one-dimensional hexagonal solid

High-order harmonic generation (HHG) from atoms is a coherent light source that opens up attosecond physics, but it is the application of HHG to solids that has brought much excitement in the last decade. Here we report a special kind of harmonics in a quasi-one-dimensional and hexagonal barium titanium sulfide: Under circularly polarized laser excitation, harmonics are generated only at first, fifth, seventh, and eleventh orders. These magic harmonics appear only with circularly polarized light, not with linearly polarized light. Neither cubic nor tetragonal cells have magic harmonics even with circularly polarized light. Through a careful group-theory analysis, we find that two subgroups of symmetry operations unique to the hexagonal symmetry cancel out third and ninth harmonics. This feature presents a rare opportunity to develop HHG into a crystal-structure characterization tool for phase transitions between hexagonal and nonhexagonal structures.