Deterministic enhancement of the superconducting (SC) critical temperature T c is a longstanding goal in material science. One strategy is engineering a material at the nanometer scale such that quantum confinement strengthens the electron pairing, thus increasing the superconducting energy gap ∆ [1-6], as was observed for individual nanoparticles [7]. A true phasecoherent SC condensate, however, can exist only on larger scales and requires a finite phase stiffness J [13]. In the case of coupled aluminium (Al) nanograins [8][9][10], T c can exceed that of bulk Al by a factor of three, but despite several proposals the relevant mechanism at play is not yet understood. Here we use optical spectroscopy on granular Al to disentangle the evolution of the fundamental SC energy scales, ∆ and J, as a function of grain coupling. Starting from wellcoupled arrays, ∆ grows with progressive grain decoupling, causing the increasing of T c . As the grain-coupling is further suppressed, ∆ saturates while T c decreases, concomitantly with a sharp decline of J. This crossover to a phase-driven SC transition is accompanied by an optical gap persisting above T c . These findings identify granular Al as an ideal playground to test the basic mechanisms that enhance superconductivity by nanoinhomogeneity.Bulk samples of pure Al represent a prototypical BCS superconductor (SC) with relatively low T c0 ≈ 1.2 K. Several studies since the late 1960s [8][9][10] have shown a quite different situation for granular Al, i.e. thin films composed of 2 nm grains separated by thin insulating barriers, where a superconducting condensate is established via Josephson-coupling across the grain array. The coupling between the grains can be controlled during film growth, leading to samples with strong coupling and low resistivity (LR) in electrical transport compared to high resistivity (HR) samples with weak intergrain coupling. In LR samples T c can be enhanced up to several times T c0 , whereas it is suppressed to zero in HR samples, shaping a superconducting dome in the phase diagram, see Fig. 1(a).To understand the behavior of T c it is crucial to access the underlying SC energy scales associated with the amplitude and phase of the complex order parameter ψ = ∆e iφ . Indeed, while the SC energy gap ∆ measures the pairing strength between the electrons, the true superfluid behavior can only be established if the Cooper pairs acquire the same macroscopic SC phase φ. The energy scale controlling the rigidity of the condensate with respect to a deformation of this collective phase-coherent state is the so-called superfluid stiffness J. In ordinary BCS superconductors J exceeds ∆ by orders of magnitudes, and the SC transition at T c is amplitude-driven. However, in the unconventional situation where ∆ exceeds J the transition is expected to be phase-driven, due to the loss of phase coherence at a temperature scale of order of J. Consequently, even though several finite-size effects have been proposed to explain the enhancement of ∆ in isolated nano-grai...

We show that the normal state transport properties of nano-scale granular Aluminum films, near the metal to insulator transition, present striking similarities with those of Kondo systems. Those include a negative magneto-resistance, a minimum of resistance R at a temperature Tm in metallic films, a logarithmic rise at low temperatures and a negative curvature of R (T ) at high temperatures. These normal state properties are interpreted in terms of spin-flip scattering of conduction electrons by local magnetic moments, possibly located at the metal/oxide interfaces. Their co-existence with the enhanced superconductivity seen in these films is discussed.PACS numbers: 74.81. Bd, 72.15.Qm Granular Al films have been known for many years to have an enhanced superconducting critical temperature. In this paper we show that in such films, conduction electrons interact with localized magnetic moments. This new finding is surprising since coexistence of an enhanced superconductivity with magnetic moments is unexpected.We present new transport measurements on aluminum films consisting of nano-scale Al grains, about 2 nm in size, weakly coupled through thin Al oxide barriers [1]. We find that near the metal to insulator transition (MIT) their magneto-resistance is increasingly negative and scales with (H/T), with an exponent close to 2, up to about 100 K. Additionally, samples having a positive resistance temperature coefficient (metallic behavior) present a minimum of resistance at a temperature T m of several 10 K depending on the film's resistivity and a temperature dependence of the resistance compatible with a logarithmic increase below T m . This logarithmic increase is more clearly seen in films whose resistance increases continuously with decreasing temperature. All metallic films near the MIT display a negative curvature of the R(T) curves. These transport properties point out to spin scattering of conducting electrons, as occurs in Kondo systems [2,3]. We discuss possible origins of localized magnetic moments and the compatibility of spin scattering of conduction electrons with the enhanced superconductivity seen in these films.Samples were prepared by thermal evaporation of 99.999% pure Al pellets from ceramic crucibles under a reduced pressure of oxygen in the range of 1 ÷ 3.5 × 10 −5 Torr. Substrates of Si − Si 2 O were cooled by liquid nitrogen during evaporation. The normal state resistivity, ρ RT , of the films was controlled by the oxygen pressure used during evaporation and by the evaporation rate.