Strange metal state near quantum superconductormetal transition in thin films
Abstract
We develop a theory of quantum T = 0 phase transition (qSMT) between metal and superconducting ground states in a twodimensional metal with frozenin spatial fluctuations δλ(r) of the Cooper attraction constant. When strength of fluctuations δλ(r) exceeds some critical magnitude, usual meanfieldlike scenario of the qSMT 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 ∕r^{β} , with 2 < β ≤ 3 . We account for this interaction by means of a realspace strongdisorder renormalization group (RG). Near the qSMT the RG flow is, formally, a dual equivalent of the KosterlitzThouless 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} ∼ 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 strongcoupling 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 Tindependent. This observation may be relevant to the understanding of a strange metal state frequently observed near qSMT.
 Publication:

Annals of Physics
 Pub Date:
 June 2020
 DOI:
 10.1016/j.aop.2020.168138
 arXiv:
 arXiv:2002.08107
 Bibcode:
 2020AnPhy.41768138T
 Keywords:

 Condensed Matter  Superconductivity;
 Condensed Matter  Mesoscale and Nanoscale Physics
 EPrint:
 To be published in Eliashberg90 special issue of Annals of Physics