  We consider non-dissipative drag between Bose-condensed exciton polaritons in
optical microcavity and embedded superconductors. This effect consists in
induction of a non-dissipative electric current in the superconductor by motion
of polariton Bose condensate due to electron-polariton interaction, or vice
versa. Using many-body theory, we calculate the drag density, characterizing
magnitude of this effect, with taking into account dynamical screening of the
interaction. Hoping to diminish the interaction screening and microcavity
photon absorption, we consider atomically-thin superconductors (both
conventional s-wave and copper-oxide d-wave) of planar and nanoribbon shapes.
Our estimates show that in realistic conditions the drag effect could be rather
weak but observable in accurate experiments in the case of dipolar interlayer
excitons in transition metal dichalcogenide bilayers. Use of spatially direct
excitons, semiconductor quantum wells as the host for excitons, or thin films
of bulk metallic superconductors considerably lowers the drag density.
