Electronic functionalities in materials from silicon to transition metal oxides are, to a large extent, controlled by defects and their relative arrangement. Outstanding examples are the oxides of copper, where defect order is correlated with their high superconducting transition temperatures. The oxygen defect order can be highly inhomogeneous, even in optimal superconducting samples, which raises the question of the nature of the sample regions where the order does not exist but which nonetheless form the "glue" binding the ordered regions together. Here we use scanning X-ray microdiffraction (with a beam 300 nm in diameter) to show that for La 2 CuO 4þy , the glue regions contain incommensurate modulated local lattice distortions, whose spatial extent is most pronounced for the best superconducting samples. For an underdoped single crystal with mobile oxygen interstitials in the spacer La 2 O 2þy layers intercalated between the CuO 2 layers, the incommensurate modulated local lattice distortions form droplets anticorrelated with the ordered oxygen interstitials, and whose spatial extent is most pronounced for the best superconducting samples. In this simplest of high temperature superconductors, there are therefore not one, but two networks of ordered defects which can be tuned to achieve optimal superconductivity. For a given stoichiometry, the highest transition temperature is obtained when both the ordered oxygen and lattice defects form fractal patterns, as opposed to appearing in isolated spots. We speculate that the relationship between material complexity and superconducting transition temperature T c is actually underpinned by a fundamental relation between T c and the distribution of ordered defect networks supported by the materials. granular superconductors | multiband superconductivity in density wave metals | scale-free heterogeneity | imaging phase separation | X-ray illumination

To account for the dark matter content in our Universe, post-inflationary scenarios predict for the QCD axion a mass in the range (10 − 10 3 ) µeV. Searches with haloscope experiments in this mass range require the monitoring of resonant cavity modes with frequency above 5 GHz, where several experimental limitations occur due to linear amplifiers, small volumes, and low quality factors of Cu resonant cavities. In this paper we deal with the last issue, presenting the result of a search for galactic axions using a haloscope based on a 36 cm 3 NbTi superconducting cavity. The cavity worked at T = 4 K in a 2 T magnetic field and exhibited a quality factor Q0 = 4.5 × 10 5 for the TM010 mode at 9 GHz. With such values of Q the axion signal is significantly increased with respect to copper cavity haloscopes. Operating this setup we set the limit gaγγ < 1.03 × 10 −12 GeV −1 on the axion photon coupling for a mass of about 37 µeV. A comprehensive study of the NbTi cavity at different magnetic fields, temperatures, and frequencies is also presented.

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The complex ac magnetic susceptibilities (χ n = χ' n + iχ n ") of high T c superconductors in absence of dc fields have been studied by numerically solving the non-linear diffusion equation for the magnetic flux, where the diffusivity is determined by the resistivity. In our approach the parallel resistor model between the creep and flux flow resistivities is used, so that the crossover between different flux dynamic processes (thermally activated flux flow, flux creep, flux flow) can naturally arise. For this reason we remark that, as the frequency increases, the presence of a different non linearity in different regions of the I-V characteristic determines nonuniversal temperature dependencies of the χ n , i.e. the χ n are found to be not universal functions of a frequency and temperature dependent single parameter. Moreover, the actual frequency dependent behavior is also shown to be strictly related to the particular pinning model chosen for the simulations. Indeed, for large values of the reduced pinning potential (U/KT≥220) and for increasing frequency, a transition has been observed between dynamic regimes dominated by creep and flux flow processes. On the other hand, for smaller reduced pinning potentials, a transition from the thermally activated flux flow (Taff) to the flow regime occurs. In qualitative agreement with available experimental data but in contrast with previously used simpler models, the amplitude of the peak of the imaginary part of the first harmonic is shown to be frequency dependent. Moreover the frequency dependence of its peak temperature shows large discrepancies with approximated analytical predictions. Finally, the shape of the temperature dependencies of the higher harmonics are found to be strongly affected by the frequency.