Substrate Induced Optical Anisotropy in Monolayer MoS$_2$

In-plane optical anisotropy has been detected from monolayer MoS$_2$ grown on a-plane (11-20) sapphire substrate in the ultraviolet-visible wavelength range. Based on the measured optical anisotropy, the energy differences between the optical transitions polarized along the ordinary and extraordinary directions of the underlying sapphire substrate have been determined. The results corroborate comprehensively with the dielectric environment induced modification on the electronic band structure and exciton binding energy of monolayer MoS$_2$ predicted recently by first principle calculations. The output of this study proposes the symmetry as a new degree of freedom for dielectric engineering of the two-dimensional materials.