Shaping a superconducting dome: Enhanced Cooper-pairing versus suppressed phase coherence in coupled aluminum nanograins

Deterministic enhancement of the superconducting (SC) critical temperature $T_c$ is a long-standing 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 $\Delta$, as was observed for individual nanoparticles. A true phase-coherent SC condensate, however, can exist only on larger scales and requires a finite phase stiffness $J$. In the case of coupled aluminium (Al) nanograins, $T_c$ 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, $\Delta$ and $J$, as a function of grain coupling. Starting from well-coupled arrays, $\Delta$ grows with progressive grain decoupling, causing the increasing of $T_c$. As the grain-coupling is further suppressed, $\Delta$ 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 nano-inhomogeneity.Comment: 6 + 6 pages (manuscript + supplementary material

Optical signatures of the superconducting Goldstone mode in granular aluminum: experiments and theory

Recent advances in the experimental growth and control of disordered thin films, heterostructures, and interfaces provide a fertile ground for the observation and characterisation of the collective superconducting excitations emerging below $T_c$ after breaking the $U(1)$ gauge symmetry. Here we combine THz experiments in a nano-structured 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 trough the sample we identify a sizeable and temperature-dependent optical sub-gap absorption, which cannot be ascribed to quasiparticle excitations. A quantitative modelling of this material as a disordered Josephson array of nano-grains 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 nanograins arrays are a promising setting to study and control the collective superconducting excitations via optical means

Charge Transfer and dddd excitations in AgF2_{2}

Charge transfer (CT) insulators are the parent phase of a large group of today's unconventional high temperature superconductors. Here we study experimentally and theoretically the interband excitations of the CT insulator silver fluoride AgF$_2$, which has been proposed as an excellent analogue of oxocuprates. Optical conductivity and resonant inelastic x-ray scattering (RIXS) on AgF$_2$ polycrystalline sample show a close similarity with that measured on undoped La$_2$CuO$_4$. While the former shows a CT gap $\sim$3.4~eV, larger than in the cuprate, $dd$-excitations are nearly at the same energy in the two materials. DFT and exact diagonalization cluster computations of the multiplet spectra show that AgF$_2$ is more covalent than the cuprate, in spite of the larger fundamental gap. Furthermore, we show that AgF$_2$ is at the verge of a charge transfer instability. The overall resemblance of our data on AgF$_2$ to those published previously on La$_2$CuO$_4$ suggests that the underlying CT insulator physics is the same, while AgF$_2$ could also benefit from a proximity to a charge density wave phase as in BaBiO$_3$. Therefore, our work provides a compelling support to the future use of fluoroargentates for materials' engineering of novel high-temperature superconductors.Comment: 13 pages, 9 Figures (including SI

Mott transition and collective charge pinning in electron doped Sr₂IrO₄

We studied the in-plane dynamic and static charge conductivity of electron doped Sr2IrO4 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

Unconventional free charge in the correlated semimetal Nd₂Ir₂O₇

Nd2Ir2O7 is a correlated semimetal with the pyrochlore structure, in which competing spin-orbit coupling and electron-electron interactions are believed to induce a time-reversal symmetry broken Weyl semimetal phase characterized by pairs of topologically protected Dirac points at the Fermi energy. However, the emergent properties in these materials are far from clear, and exotic new states of matter have been conjectured. Here we demonstrate optically that at low temperatures the free carrier spectral weight is proportional to T^2 where T is the temperature, as expected for massless Dirac electrons. However, we do {em not} observe the corresponding T^3 term in the specific heat. That the system is not in a Fermi liquid state is further corroborated by the "Planckian" T-linear temperature dependence of the momentum relaxation rate and the progressive opening of a correlation-induced gap at low temperatures. These observations can not be reconciled within the framework of band theory of electron-like quasiparticles and point toward the effective decoupling of the charge transport from the single particle sector

Mott transition and collective charge pinning in electron doped Sr2IrO4

AbstractData set corresponding to the publication Mott transition and collective charge pinning in electron doped Sr2IrO4; K. Wang, N. Bachar, J. Teyssier, W. Luo, C. W. Rischau, G. Scheerer, A. de la Torre, R. S. Perry F. Baumberger & D. van der Marel; Physical Review B 98, 045107 (2018), DOI:10.1103/PhysRevB.98.045107