High-order harmonics generated from a quasi-one-dimensional hexagonal solid*

High harmonic generation has attracted enormous attentions.
Here we report a completely new 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.

Refs.
[1] G. P. Zhang and Y. H. Bai, Phys. Rev. B {\bf 99}, 094313
(2019).
[2] Lei Jia, Zhiya Zhang, D. Z. Yang, M. S. Si, G. P. Zhang,
and Y. S. Liu, Phys. Rev. B {\bf 100}, 125144 (2019).

[3] G. P. Zhang, M. S. Si, Mitsuko Murakami, Y. H. Bai and
T. F. George, {\it Generating high-order optical and spin harmonics from
ferromagnetic monolayers}, Nat. Comm. {\bf 9}, 3031 (2018).