Extended strange metal regime from superconducting puddles

We study a model of mesoscale superconducting puddles in a metal, represented as dynamical impurities interacting with a finite number of electronic channels via Andreev and normal scattering. We  identify conditions under which the collection of puddles make a $T$-linear  contribution to the resistivity and a $T\ln(1/T)$ to the specific heat and thermopower. 

 This behavior emerges in an intermediate temperature range that extends from an upper energy scale set by the renormalized charging energy of the puddles, and down to an exponentially small scale associated with a charge-Kondo crossover, provided that the number of electronic channels interacting with the puddle is large. The phenomenology of our model resembles the 

 apparent extended strange metal regime observed in overdoped cuprates which exhibits $T$-linear resistivity at low $T$ over a finite range of doping.

We also propose to engineer a strange metal from suitably designed superconducting grains in a metallic matrix.