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 ∝ 1 ∕rβ , with 2 < β ≤ 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 Nδ ∼ 1 ∕ δ , where 0 < δ ≪ 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 ≪ 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 strange metal state frequently observed near q-SMT.
Annals of Physics
- Pub Date:
- June 2020
- Condensed Matter - Superconductivity;
- Condensed Matter - Mesoscale and Nanoscale Physics
- To be published in Eliashberg-90 special issue of Annals of Physics