Finite-momentum inter-orbital superconductivity driven by chiral charge-density-wave quantum criticality beyond the BCS regime

Superconductivity emerging near charge-density-wave (CDW) quantum critical points often defies a conventional BCS description, particularly in multi-orbital systems with small and orbitally distinct Fermi surfaces. In TiSe$_2$, superconductivity appears under pressure near the suppression of a chiral CDW, yet its microscopic origin has remained unresolved. Here we show that the chiral CDW quantum criticality in TiSe$_2$ originates from a fluctuation-induced intertwining of charge-order and phonon modes that are symmetry incompatible at the Brillouin-zone center but become mixable at the CDW ordering wave vector. This resolution of symmetry frustration enables a single continuous chiral CDW transition and strongly enhances collective fluctuations near criticality. We demonstrate that these critical chiral CDW fluctuations drive a finite-center-of-mass-momentum inter-orbital pairing instability fundamentally different from BCS superconductivity. Because electrons near the $\Gamma$ and $L$ points occupy small $p$- and $d$-orbital Fermi pockets connected only by the CDW ordering vector, the inter-orbital pair susceptibility does not develop a Cooper logarithm. As a result, superconductivity is governed by an interaction-driven pairing mechanism rather than by the density of states. Using a symmetry-constrained low-energy theory and a random-phase-approximation analysis, we show that the fluctuation-enhanced pairing interaction is maximized near the chiral CDW quantum critical point, giving rise to a dome-shaped superconducting phase. A group-theoretical analysis further identifies an orbital-selective $s$-wave pairing symmetry as the most likely superconducting state.