  We report on a novel mechanism of BCS-like superconductivity, mediated by a
pair of Bogoliubov quasiparticles (bogolons). It takes place in hybrid systems
consisting of a two-dimensional electron gas in a transition metal
dichalcogenide monolayer in the vicinity of a Bose-Einstein condensate. Taking
a system of two-dimensional indirect excitons as a testing ground we show, that
the bogolon-pair-mediated electron pairing mechanism is stronger than
phonon-mediated and single bogolon-mediated ones. We develop a microscopic
theory of bogolon-pair-mediated superconductivity, based on the
Schrieffer-Wolff transformation and the Gor'kov's equations, study the
temperature dependence of the superconducting gap and estimate the critical
temperature of superconducting transition for various concentrations of the
electron gas and the condensate densities.
