  The optical properties of two-dimensional materials are exceptional in
several respects. They are highly anisotropic and frequently dominated by
excitonic effects. Dipole-allowed second order non-linear optical properties
require broken inversion symmetry. Hence, several two-dimensional materials
show strong in-plane (IP) non-linearity but negligible out-of-plane (OOP)
response due to vertical symmetry. By considering buckled hexagonal monolayers,
we analyze the critical role of broken vertical symmetry on their excitonic
optical response. Both linear as well as second order shift current and second
harmonic response are studied. We demonstrate that substantial OOP non-linear
response can be obtained, in particular, through off-diagonal tensor elements
coupling IP excitation to OOP response. Our findings are explained by excitonic
selection rules for OOP response and the impact of dielectric screening on
excitons is elucidated.
