  We investigate electron paring in a two-dimensional electron system mediated
by vacuum fluctuations inside a nanoplasmonic terahertz cavity. We show that
the structured cavity vacuum can induce long-range attractive interactions
between current fluctuations which lead to pairing in generic materials with
critical temperatures in the low-Kelvin regime for realistic parameters. The
induced state is a pair density wave superconductor which can show a transition
from a fully gapped to a partially gapped phase - akin to the pseudogap phase
in high-$T_c$ superconductors. Our findings provide a promising tool for
engineering intrinsic electron interactions in two-dimensional materials.
