Removing electrons from the CuO 2 plane of cuprates alters the electronic correlations sufficiently to produce high-temperature superconductivity. Associated with these changes are spectral-weight transfers from the high-energy states of the insulator to low energies. In theory, these should be detectable as an imbalance between the tunneling rate for electron injection and extraction—a tunneling asymmetry. We introduce atomic-resolution tunneling-asymmetry imaging, finding virtually identical phenomena in two lightly hole-doped cuprates: Ca 1.88 Na 0.12 CuO 2 Cl 2 and Bi 2 Sr 2 Dy 0.2 Ca 0.8 Cu 2 O 8+δ . Intense spatial variations in tunneling asymmetry occur primarily at the planar oxygen sites; their spatial arrangement forms a Cu-O-Cu bond-centered electronic pattern without long-range order but with 4 a 0 -wide unidirectional electronic domains dispersed throughout ( a 0 : the Cu-O-Cu distance). The emerging picture is then of a partial hole localization within an intrinsic electronic glass evolving, at higher hole densities, into complete delocalization and highest-temperature superconductivity.

Scanning tunneling microscopy is used to image the additional quasi-particle states generated by quantized vortices in the high critical temperature superconductor Bi2Sr2CaCu2O8+delta. They exhibit a copper-oxygen bond-oriented "checkerboard" pattern, with four unit cell (4a0) periodicity and a approximately 30 angstrom decay length. These electronic modulations may be related to the magnetic field-induced, 8a0 periodic, spin density modulations with decay length of approximately 70 angstroms recently discovered in La1.84Sr0.16CuO4. The proposed explanation is a spin density wave localized surrounding each vortex core. General theoretical principles predict that, in the cuprates, a localized spin modulation of wavelength lambda should be associated with a corresponding electronic modulation of wavelength lambda/2, in good agreement with our observations.

In the high-transition-temperature (high-T(c)) superconductors the pseudogap phase becomes predominant when the density of doped holes is reduced. Within this phase it has been unclear which electronic symmetries (if any) are broken, what the identity of any associated order parameter might be, and which microscopic electronic degrees of freedom are active. Here we report the determination of a quantitative order parameter representing intra-unit-cell nematicity: the breaking of rotational symmetry by the electronic structure within each CuO(2) unit cell. We analyse spectroscopic-imaging scanning tunnelling microscope images of the intra-unit-cell states in underdoped Bi(2)Sr(2)CaCu(2)O(8 +) (delta) and, using two independent evaluation techniques, find evidence for electronic nematicity of the states close to the pseudogap energy. Moreover, we demonstrate directly that these phenomena arise from electronic differences at the two oxygen sites within each unit cell. If the characteristics of the pseudogap seen here and by other techniques all have the same microscopic origin, this phase involves weak magnetic states at the O sites that break 90 degrees -rotational symmetry within every CuO(2) unit cell.

The phase diagram of hole-doped copper oxides shows four different electronic phases existing at zero temperature. Familiar among these are the Mott insulator, high-transition-temperature superconductor and metallic phases. A fourth phase, of unknown identity, occurs at light doping along the zero-temperature bound of the 'pseudogap' regime 1 . This regime is rich in peculiar electronic phenomena 1 , prompting numerous proposals that it contains some form of hidden electronic order. Here we present low-temperature electronic structure imaging studies of a lightly hole-doped copper oxide: Ca 2−x Na x CuO 2 Cl 2 . Tunnelling spectroscopy (at energies |E|>100 meV) reveals electron extraction probabilities greatly exceeding those for injection, as anticipated for a doped Mott insulator. However, for |E|<100 meV, the spectrum exhibits a V-shaped energy gap centred on E=0. States within this gap undergo intense spatial modulations, with the spatial correlations of a four CuO 2 -unit-cell square 'checkerboard', independent of energy. Intricate atomic-scale electronic structure variations also exist within the checkerboard. These data are consistent with an unanticipated crystalline electronic state, possibly the hidden electronic order, existing in the zero-temperature pseudogap regime of Ca 2−x Na x CuO 2 Cl 2 .Scanning tunnelling microscopy (STM) has recently emerged as a suitable technique to search for 'hidden' electronic order in the copper oxides. Bi 2 Sr 2 CaCu 2 O 8+δ (Bi-2212) studies where high-transition-temperature (T c ) superconductivity (HTSC) was 2 suppressed to reveal the pseudogap have been especially fruitful. The prototypical study yielded a pseudogap-like conductance spectrum (V-shaped without coherence peaks) associated with a 'checkerboard' approximately four CuO 2 unit cells square of localdensity-of-states (LDOS) modulations surrounding vortex cores 2 . Similar phenomena were discovered throughout the sample above T c (ref.3), and within strongly underdoped nano-regions exhibiting pseudogap-like spectra 4 (see Fig. 1c). Underdoped Bi-2212 therefore shows a tendency towards checkerboard electronic modulations when HTSC is suppressed. However, it is unclear whether these checkerboard modulations in Bi-2212 represent a true electronic phase, because they exhibit [2][3][4] (1) a variety of dopingdependent incommensurate wavevectors, (2) very weak intensities, and (3) To search for electronic order hidden in the pseudogap while avoiding these uncertainties, we decided to study a simpler and less disordered copper oxide at lower doping and temperature. We chose Ca 2−x Na x CuO 2 Cl 2 (Na-CCOC), a material whose parent compound Ca 2 CuO 2 Cl 2 is a canonical Mott insulator 8 . Within its undistorted tetragonal crystal structure (Fig. 1b), all the CuO 2 planes are crystallographically identical. Sodium substitution for Ca destroys the Mott insulator state, producing first a nodal metal 9 in the zero-temperature pseudogap (ZTPG) regime, and eventually HTSC for x≥0. 10 (refs 10, 11). Crucially, Na-CCOC ...

Although the crystal structures of the copper oxide high-temperature superconductors are complex and diverse, they all contain some crystal planes consisting of only copper and oxygen atoms in a square lattice: superconductivity is believed to originate from strongly interacting electrons in these CuO2 planes. Substituting a single impurity atom for a copper atom strongly perturbs the surrounding electronic environment and can therefore be used to probe high-temperature superconductivity at the atomic scale. This has provided the motivation for several experimental and theoretical studies. Scanning tunnelling microscopy (STM) is an ideal technique for the study of such effects at the atomic scale, as it has been used very successfully to probe individual impurity atoms in several other systems. Here we use STM to investigate the effects of individual zinc impurity atoms in the high-temperature superconductor Bi2Sr2CaCu2O8+delta. We find intense quasiparticle scattering resonances at the Zn sites, coincident with strong suppression of superconductivity within approximately 15 A of the scattering sites. Imaging of the spatial dependence of the quasiparticle density of states in the vicinity of the impurity atoms reveals the long-sought four-fold symmetric quasiparticle 'cloud' aligned with the nodes of the d-wave superconducting gap which is believed to characterize superconductivity in these materials.

Granular superconductivity occurs when microscopic superconducting grains are separated by non-superconducting regions through which they communicate by Josephson tunneling to establish the macroscopic superconducting state 1 . Although crystals of the cuprate high-T c superconductors are not granular in a structural sense, theory indicates that at low hole densities the holes can become concentrated at some locations resulting in hole-rich superconducting domains 2-5 . Granular superconductivity due to Josephson tunneling through 'undoped' regions between such domains would represent a new paradigm for the underdoped cuprates. Here we report studies of the spatial interrelationships between STM tunneling spectra in underdoped Bi 2 Sr 2 CaCu 2 O 8+d . They reveal an apparent spatial segregation of the electronic structure into ~3nm diameter domains (with superconducting characteristics and local energy gap ∆<50 meV) in an electronically distinct background. To explore whether this represents nanoscale segregation of two distinct electronic phases, we employ scattering-resonances at Ni impurity atoms 6 as 'markers' for the local existence of superconductivity [7][8][9] . No Ni-resonances are detected in any regions where ∆>50±2.5 meV. These observations suggest that underdoped Bi 2 Sr 2 CaCu 2 O 8+d is a mixture of two different short-range electronic orders with the long-range characteristics of a granular superconductor.

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.

Scanning tunneling spectroscopy of the high-Tc superconductor Bi2Sr2CaCu2O8+delta reveals weak, incommensurate, spatial modulations in the tunneling conductance. Images of these energy-dependent modulations are Fourier analyzed to yield the dispersion of their wavevectors. Comparison of the dispersions with photoemission spectroscopy data indicates that quasiparticle interference, due to elastic scattering between characteristic regions of momentum-space, provides a consistent explanation for the conductance modulations, without appeal to another order parameter. These results refocus attention on quasiparticle scattering processes as potential explanations for other incommensurate phenomena in the cuprates. The momentum-resolved tunneling spectroscopy demonstrated here also provides a new technique with which to study quasiparticles in correlated materials.