The antiferromagnetic ground state of copper oxide Mott insulators is achieved by localizing an electron at each copper atom in real space (r-space). Removing a small fraction of these electrons (hole doping) transforms this system into a superconducting fluid of delocalized Cooper pairs in momentum space (k-space). During this transformation, two distinctive classes of electronic excitations appear. At high energies, the mysterious 'pseudogap' excitations are found, whereas, at lower energies, Bogoliubov quasi-particles-the excitations resulting from the breaking of Cooper pairs-should exist. To explore this transformation, and to identify the two excitation types, we have imaged the electronic structure of Bi(2)Sr(2)CaCu(2)O(8+delta) in r-space and k-space simultaneously. We find that although the low-energy excitations are indeed Bogoliubov quasi-particles, they occupy only a restricted region of k-space that shrinks rapidly with diminishing hole density. Concomitantly, spectral weight is transferred to higher energy r-space states that lack the characteristics of excitations from delocalized Cooper pairs. Instead, these states break translational and rotational symmetries locally at the atomic scale in an energy-independent way. We demonstrate that these unusual r-space excitations are, in fact, the pseudogap states. Thus, as the Mott insulating state is approached by decreasing the hole density, the delocalized Cooper pairs vanish from k-space, to be replaced by locally translational- and rotational-symmetry-breaking pseudogap states in r-space.

The randomness of dopant atom distributions in cuprate high-critical temperature superconductors has long been suspected to cause nanoscale electronic disorder. In the superconductor Bi2Sr2CaCu2O8+delta, we identified populations of atomic-scale impurity states whose spatial densities follow closely those of the oxygen dopant atoms. We found that the impurity-state locations are strongly correlated with all manifestations of the nanoscale electronic disorder. This disorder occurs via an unanticipated mechanism exhibiting high-energy spectral weight shifts, with associated strong superconducting coherence peak suppression but very weak scattering of low-energy quasi-particles.

The mechanism of high-temperature superconductivity in the newly discovered iron-based superconductors is unresolved. We use spectroscopic imaging-scanning tunneling microscopy to study the electronic structure of a representative compound CaFe1.94Co0.06As2 in the "parent" state from which this superconductivity emerges. Static, unidirectional electronic nanostructures of dimension eight times the inter-iron-atom distance a(Fe-Fe) and aligned along the crystal a axis are observed. In contrast, the delocalized electronic states detectable by quasiparticle interference imaging are dispersive along the b axis only and are consistent with a nematic alpha2 band with an apparent band folding having wave vector q vector congruent with +/-2pi/8a(Fe-Fe) along the a axis. All these effects rotate through 90 degrees at orthorhombic twin boundaries, indicating that they are bulk properties. As none of these phenomena are expected merely due to crystal symmetry, underdoped ferropnictides may exhibit a more complex electronic nematic state than originally expected.

Nowadays, energetic needs are mainly covered by fossil fuels with concomitant pollutant emissions responsible for global warming. Among the possible solutions to reduce the greenhouse effect, hydrogen has been proposed for energy transportation. Indeed, this gas can be seen as a clean and efficient energy carrier. However, besides the difficulties related to hydrogen production, high-capacity storage is still to be developed. Hydrogen can be stored as a compressed gas, liquefied in tanks, and ab-or adsorbed in solids.[1-3] Many compounds are able to store large amounts of hydrogen. Such solid-state solutions are of interest in terms of safety, global yield, and long-term storage. However, to be suitable for applications, such compounds must have high capacity, good reversibility, fast reactivity, and sustainability. Two different approaches are possible for solid-state storage of hydrogen. In the first, the hydrogen molecule is dissociated and H atoms form chemical bonds with the solid (chemisorption). Such a process allows a very high volumetric density at temperatures and pressures close to ambient conditions. However, storage in metal hydrides has the drawback of low weight capacities, essentially due to the high molar mass of heavy metals such as

. † These authors contributed equally to this project. The existence of electronic symmetry breaking in the underdopedcuprates, and its disappearance with increased hole-density p, are now widely reported. However, the relationship between this transition and the momentumspace ( ⃗ -space) electronic structure underpinning the superconductivity has not been established. Here we visualize the ⃗ =0 (intra-unit-cell) and ⃗ ≠0 (density wave) broken-symmetry states simultaneously with the coherent ⃗ -space topology, for Bi2Sr2CaCu2O8+d samples spanning the phase diagram 0.06≤p≤0.23.We show that the electronic symmetry breaking tendencies weaken with increasing p and disappear close to pc=0.19. Concomitantly, the coherent ⃗ -space topology undergoes an abrupt transition, from arcs to closed contours, at the same pc. These data reveal that the ⃗ -space topology transformation in cuprates is linked intimately with the disappearance of the electronic symmetry breaking at a concealed critical point. 2The highest known superconducting critical temperature Tc (1-3) occurs atop the Tc(p) 'dome' of hole-doped cuprates (Fig. 1A). In addition to the superconductivity, electronic broken-symmetry states (4) have also been reported at low p in many such compounds. Wavevector ⃗ =0 (intra-unit-cell) symmetry breaking, typically of 90 orotational (C4) symmetry, is reported in YBa2Cu3O6+, . Finite wavevector ⃗ ≠0 (density wave) modulations breaking translational symmetry, long detected in underdoped 16), are now also reported in underdoped YBa2Cu3O6+, . Summarizing all such reports in Fig. 1A reveals some stimulating observations.First, although the ⃗ =0 and ⃗ ≠0 states are detected by widely disparate techniques and are distinct in terms of symmetry, they seem to follow approximately the same phasediagram trajectory (shaded band Fig. 1A) as if facets of a single phenomenon (26). The second implication is that a critical point (perhaps a quantum critical point) associated with these broken-symmetry states may be concealed beneath the Tc(p) dome.Numerous earlier studies reported sudden alterations in many electronic/magnetic characteristics near p=0.19 (2,3,27), but whether these phenomena are caused by electronic symmetry changes (28) at a critical point was unknown. 3In ⃗ -space, the hole-doped cuprates also exhibit an unexplained transition in electronic structure with increasing hole density. Open contours or "Fermi arcs" (29)(30)(31)(32) are reported at low p in all compounds studied, while at high p closed hole-like pockets surrounding ⃗ = (±1, ±1) / 0 are observed (33,34). One possibility is that such a transition could occur due to the disappearance of an electronic ordered state, with the resulting modifications to the Brillouin zone geometry altering the topology of the electronic bands (28). 4Our strategy is therefore a simultaneous examination of both the ⃗ -space 11,36) or at the Bragg wavevectors (11,26,35). But the complete doping dependence of these broken-symmetry signatures was unknown. 6To determine the ⃗ -space t...

Formation of electron pairs is essential to superconductivity. For conventional superconductors, tunnelling spectroscopy has established that pairing is mediated by bosonic modes (phonons); a peak in the second derivative of tunnel current d2I/dV2 corresponds to each phonon mode. For high-transition-temperature (high-T(c)) superconductivity, however, no boson mediating electron pairing has been identified. One explanation could be that electron pair formation and related electron-boson interactions are heterogeneous at the atomic scale and therefore challenging to characterize. However, with the latest advances in d2I/dV2 spectroscopy using scanning tunnelling microscopy, it has become possible to study bosonic modes directly at the atomic scale. Here we report d2I/dV2 imaging studies of the high-T(c) superconductor Bi2Sr2CaCu2O8+delta. We find intense disorder of electron-boson interaction energies at the nanometre scale, along with the expected modulations in d2I/dV2 (refs 9, 10). Changing the density of holes has minimal effects on both the average mode energies and the modulations, indicating that the bosonic modes are unrelated to electronic or magnetic structure. Instead, the modes appear to be local lattice vibrations, as substitution of 18O for 16O throughout the material reduces the average mode energy by approximately 6 per cent--the expected effect of this isotope substitution on lattice vibration frequencies. Significantly, the mode energies are always spatially anticorrelated with the superconducting pairing-gap energies, suggesting an interplay between these lattice vibration modes and the superconductivity.

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We present studies of the electronic structure of La(2-x)BaxCuO4, a system where the superconductivity is strongly suppressed as static spin and charge orders or "stripes" develop near the doping level of x = (1/8). Using angle-resolved photoemission and scanning tunneling microscopy, we detect an energy gap at the Fermi surface with magnitude consistent with d-wave symmetry and with linear density of states, vanishing only at four nodal points, even when superconductivity disappears at x = (1/8). Thus, the nonsuperconducting, striped state at x = (1/8) is consistent with a phase-incoherent d-wave superconductor whose Cooper pairs form spin-charge-ordered structures instead of becoming superconducting.