Deconfined Fermi liquid to Fermi liquid transition and superconducting instability

Deconfined quantum critical points have attracted lots of attention in the past decades but were mainly restricted to incompressible phases. On the other hand, various experimental puzzles call for a new theory of unconventional quantum criticality between metals at a generic density. Here we explore the possibility of a deconfined transition between two symmetric Fermi liquids (FLs) in a bilayer model tuned by interlayer antiferromagnetic spin-spin coupling $J_{\perp }$. Across the transition the Fermi-surface volume per flavor jumps by $1/2$ of the Brillouin zone, similar to the small to large Fermi-surface transitions in heavy fermion systems and maybe also in the high $T_{\text{c}}$ cuprates. But in the bilayer case the small Fermi-surface phase (dubbed sFL) has neither symmetry breaking nor fractionalization, akin to the symmetric mass generation discussed in high-energy physics. We formulate a deconfined critical theory where the two Fermi liquids correspond to Higgs and/or confined phases of a $\text{U}\left(1\right)\times \text{U}\left(1\right)$ gauge theory. We show that this deconfined FL to FL transition fixed point is unstable to pairing and thus a superconductor dome is expected at low temperature. At finite temperature above the pairing scale, microscopic electron is a composite of three deconfined fractional fermions in the critical theory. We also introduce another parameter which can suppress the pairing instability, leading to a deconfined phase stable to zero temperature. Our work opens a direction to exploring deconfined metallic criticality and pairing mechanism from critical gauge field. The transition may be relevant to the recently found nickelate superconductor ${\mathrm{La}}_3{\mathrm{Ni}}_2{O}_7$ and future experiments in bilayer optical lattice.