Spin Hall effect for polaritons in a TMDC monolayer embedded in a microcavity*

The spin Hall effect (SHE) for polaritons in a transition metal dichalcogenides (TMDC) monolayer embedded in a microcavity is predicted. We demonstrate that two counterpropagating laser beams incident on a TMDC monolayer can deflect a polariton flow due to generation the effective gauge vector and scalar potentials. The components of polariton conductivity tensor for a weakly-interacting Bose gas of polaritons in the presence of Bose-Einstein condensation (BEC) and superfluidity and for non-interacting polaritons without BEC are obtained. We propose to study the superfluidity of microcavity polaritons by experimental measurement of components of a total conductivity tensor as functions of the effective gauge magnetic field at different temperatures. It is shown that the concentrations of the normal and superfluid components and the Kosterlitz-Thouless temperature of occurrence of superfluidity can be determined by experimental measurement the components of the total conductivity tensor. The possible experimental observation of the SHE for microcavity polaritons is proposed, which provides the signature of the superfluidity of microcavity polaritons.