Skew scattering and ratchet effect in photonic graphene

The present paper is devoted to a comprehensive theoretical study of asymmetric (skew) scattering in photonic graphene, with the main focus on its realization with semiconductor microcavity exciton-polaritons. As an important consequence of the skew scattering, we prove the appearance of the ratchet effect in this system. Triangular defects in the form of missing micropillars in a regular honeycomb lattice are considered as ones that break the spatial inversion symmetry, thus providing the possibility of the ratchet effect. By means of the numerical solution of the effective Schr\"odinger equation, we provide microscopical insight into the process of skew scattering and determine indicatrices, cross-sections, and asymmetry parameters. In a system with multiple coherently oriented triangular defects, a macroscopic ratchet effect occurs as a unidirectional flux upon noise-like initial conditions. Our study broadens the concept of ratchet phenomena in the field of photonics and optics of exciton-polaritons.