Title: Interface and bulk superconductivity in superconducting heterostructures with enhanced critical temperatures

Abstract: We consider heterostructures obtained by stacking layers of two s-wave superconductors with significantly different coupling strengths, respectively in the weak- and strong-coupling regimes. The weak- and strong-coupling superconductors are chosen with similar critical temperatures for bulk systems. Using dynamical mean-field theory methods, we find an ubiquitous enhancement of the superconducting critical temperature for all the heterostructures where a single layer of one of the two superconductors is alternated with a thicker multilayer of the other. Two distinct physical regimes can be identified as a function of the thickness of the larger layer: (i) an inherently inhomogeneous superconductor characterized by the properties of the two isolated bulk superconductors where the enhancement of the critical temperature is confined to the interface and (ii) a bulk superconductor with an enhanced critical temperature extending to the whole heterostructure. We characterize the crossover between these regimes in terms of the competition between two length scales connected with the proximity effect and the pair coherence.