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.

The presence of free spins in granular Al films is directly demonstrated by µSR measurements. A Mott transition is observed by probing the increase of the spin-flip scattering rate of conduction electrons as the nano-size metallic grains are being progressively decoupled. Analysis of the magnetoresistance in terms of an effective Fermi energy shows that it becomes of the order of the grains electrostatic charging energy at a room temperature resistivity ρ ≈ 50, 000 µΩ cm, at which a metal to insulator transition is known to exist. As this transition is approached the magneto-resistance exhibits a Heavy-Fermion like behavior, consistent with an increased electron effective mass.PACS numbers: 74.81. Bd, 71.30.+h, 72.15.Qm, 74.25.Ha Thanks to advances in the development of the Density functional Mean Field Theory (DMFT) [1], considerable advances have been made in recent years towards a detailed understanding of the Mott metal to insulator transition, predicted to occur when the electron-electron interaction is of the order of the bandwidth [2]. However the experimental observation of this transition has remained a challenge in three dimensional systems. This is because in a homogeneous metal the Coulomb interaction is by several orders of magnitude smaller than the bandwidth, even in the presence of a relatively high concentration of impurities [3,4].We show here that a Mott transition takes place in granular metals, as nano-size grains are being decoupled from each other by a progressive reduction of the intergrain tunneling probability. Two of the main features of this transition predicted by DMFT theory, an increase of the electron effective mass and a non-critical behavior of the electronic density of states as the transition is approached, have been observed. These observations have been made possible by the presence of free spins in granular Aluminum films, which we confirm here by direct µSR measurements. Interaction of these spins with conduction electrons results in a negative magneto-resistance [5]. We have used it as a tool to follow changes of the effective Fermi energy of the granular medium as the transition is being approached. When it occurs, at a room temperature resistivity of about 50,000 µΩcm, we find that the effective Fermi energy is of the order of the grain's charging electrostatic energy. The superconducting critical temperature of the films remains relatively high up to close to the transition, indicating there is no drastic reduction of the density of states up to the transition.Low energy muon spin rotation/relaxation (LE µSR) experiments [6] were performed on film not too close to the MIT transition. The measurements were performed at the Swiss Muon Source on the µE4 beam-line, at the Paul Scherrer Institute, in Switzerland. With implantation energy of 10 keV all the muons stop in the 100 nm FIG. 1. Temperature dependence of the muon spin relaxation rate of electronic origin λ for a sample with ρ300K ≈ 140 µΩcm. λ appears to saturate around a temperature where ρ(T ) starts to increa...

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Recent advances in the experimental growth and control of disordered thin films, heterostructures, and interfaces provide fertile ground for the observation and characterization of the collective superconducting excitations emerging below Tc after breaking the U(1) gauge symmetry. Here we combine THz experiments in a nanostructured granular Al thin film and theoretical calculations to demonstrate the existence of optically active phase modes, which represent the Goldstone excitations of the broken gauge symmetry. By measuring the complex transmission through the sample we identify a sizable and temperature-dependent optical subgap absorption, which cannot be ascribed to quasiparticle excitations. A quantitative modeling of this material as a disordered Josephson array of nanograins allows us to determine, with no free parameters, the structure of the spatial inhomogeneities induced by shell effects. Besides being responsible for the enhancement of the critical temperature with respect to bulk Al, already observed in the past, this spatial inhomogeneity provides a mechanism for the optical visibility of the Goldstone mode. By computing explicitly the optical spectrum of the superconducting phase fluctuations we obtain a good quantitative description of the experimental data. Our results demonstrate that nanograin arrays are a promising setting to study and control the collective superconducting excitations via optical means

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We studied the in-plane dynamic and static charge conductivity of electron doped Sr 2 IrO 4 using optical spectroscopy and DC transport measurements. The optical conductivity indicates that the pristine material is an indirect semiconductor with a direct Mott gap of 0.55 eV. Upon substitution of 2% La per formula unit the Mott gap is suppressed except in a small fraction of the material (15%) where the gap survives, and overall the material remains insulating. Instead of a zero energy mode (or Drude peak) we observe a soft collective mode (SCM) with a broad maximum at 40 meV. Doping to 10% increases the strength of the SCM, and a zero-energy mode occurs together with metallic DC conductivity. Further increase of the La substitution doesn't change the spectral weight integral up to 3 eV. It does however result in a transfer of the SCM spectral weight to the zero-energy mode, with a corresponding reduction of the DC resistivity for all temperatures from 4 to 300 K. The presence of a zero-energy mode signals that at least part of the Fermi surface remains ungapped at low temperatures, whereas the SCM appears to be caused by pinning a collective frozen state involving part of the doped electrons.

We report measurements of the Nernst effect and of the magneto-resistance of granular aluminum films near the metal to insulator transition. These films show sharp transitions as a function of temperature and magnetic field. At low temperatures the Nernst signal displays a sharp peak at a field where more than 90% of the normal state resistance has been restored, suggesting a transition involving entropy transport after superconducting coherence has been destroyed. At temperatures higher than the critical temperature the fluctuation paraconductivity scales with the Nernst signal, in agreement with a description in terms of fluctuations of the order parameter.