BCS superconductivity in the presence of wave dark matter

In the established era of dark matter, condensed matter Hamiltonians-including those of superconductors-may require extension to account for the surrounding Galactic environment. We show that if dark matter is wave-like and couples weakly to electrons, superconducting parameters such as the gap and critical temperature become dynamical quantities that oscillate in time. This modifies the Bardeen-Cooper-Schrieffer framework and produces distinctive temporal signatures whose sensitivity increases with longer measurement durations. Our results illustrate how condensed matter systems, traditionally treated as isolated from their cosmological environment, may acquire new dynamical degrees of freedom from their cosmic embedding. This, in turn, offers a novel window into the dark sector.