It has recently been established that the high temperature (high-Tc(between atomic and macroscopic scale). Here we report micro X-ray diffraction imaging of the spatial distribution of both the charge-density-wave 'puddles' (domains with only a few wavelengths) and quenched disorder in HgBa 2 CuO 4+y , the single layer cuprate with the highest T c , 95 kelvin [26][27][28] . We found that the charge-density-wave puddles, like the steam bubbles in boiling water, have a fat-tailed size distribution that is typical of selforganization near a critical point 19 . However, the quenched disorder, which arises from oxygen interstitials, has a distribution that is contrary to the usual assumed random, uncorrelated distribution 12, 13 . The interstitials-oxygen-rich domains are spatially anticorrelated with the charge-density-wave domains, leading to a complex emergent geometry of the spatial landscape for superconductivity. 2Although it is known that the incommensurate charge-density-wave (CDW) order in cuprates (copper oxides) is made of ordered, stripy, nanoscale puddles with an average of only 3-4 oscillations, information about the size distribution and spatial organization of these puddles has so far not been available. We present experiments that demonstrate that CDW puddles, have a complex spatial distribution and coexist with, but are spatially anticorrelated to, quenched disorder in HgBa 2 CuO 4+y (Hg1201). The sample we studied is a layered perovskite at optimum doping with oxygen interstitials y=0.12, tetragonal symmetry P4/mmm and a low misfit strain [14][15][16] . The X-ray diffraction (XRD) measurements (see Methods) show diffuse CDW satellites (secondary peaks surrounding a main peak) at q CDW =(0.23a*, 0.16c*), in the b*=0 plane and q CDW =(0.23b*, 0.16c*) in the a*=0 plane (where a*, b*, and c* are the reciprocal lattice units) around specific Bragg peaks, such as (1 0 8), below the onset temperature T CDW =240 K (see Fig. 1a). The component of the momentum transfer q CDW in the CuO 2 plane (0.23a*) in this case is smaller than it is in the underdoped case (0.28a*) 5 . The temperature evolution of CDW-peak profile along a* (in the h direction; Fig. 1b) shows a smeared, glassy-like evolution below T CDW .The CDW-peak intensity reaches a maximum at T=100 K, followed by a drop associated with the onset of superconductivity at T=T c . We investigated the isotropic character of the CDW, in the a-b plane using azimuthal scans, as shown in Fig. 1c. We observed an equal probability of vertical and horizontally striped CDW puddles.Our main result is the discovery of the statistical spatial distribution of the CDW-puddle size and density throughout the sample, which shows an emergent complex network geometry for the superconducting phase. We performed scanning micro X-ray diffraction (SµXRD) measurements (see Methods) to extend the imaging of spatial inhomogeneity previously obtained by scanning tunneling microscopy [7][8][9] , from the surface to the bulk of the sample and from nanoscale to mesoscale spatial inh...

The electronic structure of graphene on Cu(111) and Cu(100) single crystals is investigated using low energy electron microscopy, low energy electron diffraction and angle resolved photoemission spectroscopy. On both substrates the graphene is rotationally disordered and interactions between the graphene and substrate lead to a shift in the Dirac crossing of ∼ -0.3 eV and the opening of a ∼ 250 meV gap. Exposure of the samples to air resulted in intercalation of oxygen under the graphene on Cu(100), which formed a (superstructure. The effect of this intercalation on the graphene π bands is to increase the offset of the Dirac crossing (∼ -0.6 eV) and enlarge the gap (∼ 350 meV). No such effect is observed for the graphene on Cu (111) sample, with the surface state at Γ not showing the gap associated with a surface superstructure. The graphene film is found to protect the surface state from air exposure, with no change in the effective mass observed, as for 1 monolayer of Ag on Cu(111).

Resonances in the superconducting properties, in a regime of crossover from BCS to mixed Bose-Fermi superconductivity, are investigated in a two-band superconductor where the chemical potential is tuned near the band edge of the second miniband generated by quantum confinement effects. The shape resonances at T=0 in the superconducting gaps (belonging to the class of Feshbach-like resonances) is manifested by interference effects in the superconducting gap at the first large Fermi surface when the chemical potential is in the proximity of the band edge of the second miniband. The case of a superlattice of quantum wells is considered and the amplification of the superconducting gaps at the Lifshitz transition of the type neck-collapsing of Fermi surface topology is clearly shown. The results are found to be in good agreement with available experimental data on a superlattice of honeycomb boron layers intercalated by Al and Mg spacer layers