Pairing of two-dimensional fermions due to singular interactions

We study a finite-temperature spectrum renormalization and s-wave pairing instability in a system of fermions with an attractive ‘‘current-current’’ interaction mediated by an overdamped mode with a dispersion ω=i${\mathrm{\Gamma }}^{\mathrm{-}1}$ ${\mathit{q}}^{2+\mathrm{\eta }}$, 0≤η≤1. It generalizes the case of a transverse gauge interaction between spinons in Mott insulators, which drives an instability of a homogeneous resonant valence bond state towards a dimerization.