Smectic Superconductivity

Abstract

We identify a mechanism in which soft nonunitary fluctuations of the pair condensate can suppress phase coherence in a two-dimensional Rashba superconductor proximate to easy-plane ferromagnetic order. This spin polarization couples linearly to the supercurrent through a Lifshitz invariant, acting as an emergent gauge field for the superconducting $\mathrm{U}(1)$ phase. Integrating out soft magnetic fluctuations renormalizes the effective superfluid stiffness and drives the system into a "smectic" superconducting state, characterized by a finite-momentum helical phase texture and a long-wavelength stiffness that vanishes in one direction. Consequently, vortices no longer have a logarithmically divergent energy cost, and the quasi-long-range superconducting order is destroyed at any finite temperature. Weak lattice anisotropy pins the ferromagnetic order, cutting off the smectic-like behaviour at long wavelengths and thereby restoring a finite effective stiffness. Nonetheless, near the onset of magnetic order, the enhanced magnetic susceptibility leads to a vortex-deconfined regime for arbitrarily weak magnetoelectric coupling. The results provide insight into how intertwined superconducting and easy-plane ferromagnetic orders can reshape phase coherence, with relevance to rhombohedral graphene proximitized by a transition-metal dichalcogenide substrate.