Strange metal state near quantum superconductor-metal transition in thin films

Abstract

We develop a theory of quantum $T = 0$ phase transition (q-SMT) between metal and superconducting ground states in a two-dimensional metal with frozen-in spatial fluctuations $δλ(r)$ of the Cooper attraction constant. When strength of fluctuations $δλ(r)$ exceeds some critical magnitude, usual mean-field-like scenario of the q-SMT breaks down due to spontaneous formation of local droplets of superconducting phase. The density of these droplets grows exponentially with the increase of average attraction constant $λ$. Interaction between the droplet's order parameters is due to proximity effect via normal metal and scales with distance $\propto 1/r^β$ , with $2 < β\le 3$. We account for this interaction by means of a real-space strong-disorder renormalization group (RG). Near the q-SMT the RG flow is, formally, a dual equivalent of the Kosterlitz-Thouless RG. The corresponding line of fixed points describes a Griffiths phase of a metal with large fractal clusters of superconducting islands. Typical number of islands in a cluster grows as $N_δ\sim 1/δ$, where $0 < δ\ll 1 $ is the distance to the critical point. Superconducting side is described by a runaway of RG trajectories into the strong-coupling region. Close to the transition point on the SC side, $0<-δ\ll 1$, RG trajectories possess an extremum as function of the RG parameter $|δ|^{1/2} \ln(1/Tτ)$. It results in a wide temperature range where physical properties are nearly $T$-independent. This observation may be relevant to the understanding of a \emph{strange metal} state frequently observed near q-SMT.