Finite-wavevector instability in dense hydrogen from electronic screening

I demonstrate that dense hydrogen, modeled as a coupled proton–electron fluid within a minimal density-functional framework, exhibits a generic instability of the homogeneous metallic state toward density modulation at finite wavevector 𝑘0. The instability originates from the competition between ionic gradient stiffness and the nonlocal electronic response function evaluated within the random-phase approximation (RPA).I derive an explicit criterion for the onset of the instability and show that the inverse ionic susceptibility develops a minimum at nonzero 𝑘0, leading to a Brazovskii-type ordering transition. My result provides a universal mechanism for intermediate-scale density ordering in compressed Coulomb systems.