  We theoretically investigate charge transport through electronic bands of a
mesoscopic one-dimensional system, where inter-band transitions are coupled to
a confined cavity mode, initially prepared close to its vacuum. This coupling
leads to light-matter hybridization where the dressed fermionic bands interact
via absorption and emission of dressed cavity-photons. Using a self-consistent
non-equilibrium Green's function method, we compute electronic transmissions
and cavity photon spectra and demonstrate how light-matter coupling can lead to
an enhancement of charge conductivity in the steady-state. We find that
depending on cavity loss rate, electronic bandwidth, and coupling strength, the
dynamics involves either an individual or a collective response of Bloch
states, and explain how this affects the current enhancement. We show that the
charge conductivity enhancement can reach orders of magnitudes under
experimentally relevant conditions.
