Unconventional Bloch-Gr\"{u}neisen scattering in hybrid Bose-Fermi systems

We report on the novel mechanism of electron scattering in hybrid Bose-Fermi systems consisting of a two-dimensional electron gas in the vicinity of an exciton condensate: We show that a pair-of-bogolons--mediated scattering proves to be dominating over the conventional acoustic phonon channel and over the single-bogolon scattering, even if the screening is taken into account. We develop a microscopic theory of this effect, focusing on GaAs and MoS$_2$ materials, and find the principal temperature dependence of resistivity, distinct from the conventional phonon--mediated processes. Further, we scrutinize parameters and suggest a way to design composite samples with predefined electron mobilities and propose a mechanism of electron pairing for superconductivity.