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.

An understanding of the nature of superconductivity in cuprates has been hindered by the apparent diversity of intertwining electronic orders in these materials. Here we combine resonant X-ray scattering (REXS), scanning-tunneling microscopy (STM), and angle-resolved photoemission spectroscopy (ARPES) to observe a charge order that appears consistently in surface and bulk, as well as momentum and real space, with the Bi2Sr2−xLaxCuO 6+δ cuprate family. The observed wavevector rules out simple antinodal nesting in the single particle limit, but matches well with a phenomenological model of a many-body instability of the Fermi arcs. Combined with earlier observations in other cuprate families, these findings suggest the existence of a generic charge-ordered state in underdoped cuprates, and uncover its connection to the pseudogap regime. PACS numbers:Since the discovery of cuprate high-temperature superconductors, several unconventional phenomena have been observed in the region of the phase diagram located between the strongly localized Mott insulator at zero doping and the itinerant Fermi-liquid state that emerges beyond optimal doping [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. The so-called 'pseudogap' opens at the temperature T * and obliterates the Fermi surface at the antinodes (AN) of the d-wave superconducting gap function, leaving behind disconnected "Fermi arcs" centered around the nodes. In addition, charge order has been observed on the surface of Bi-and Clbased compounds [4][5][6][7][8], in the bulk of La-based compounds [9][10][11], and most recently in YBa 2 Cu 3 O 6+δ (YBCO) [17][18][19][20], indicating this might be the leading instability in underdoped cuprates. The similarity between the observed charge ordering wavevector and the antinodal nesting vector of the hightemperature Fermi surface has prompted suggestions that a conventional Peierls-like charge-density-wave (CDW) might be responsible for the opening of the pseudogap [7,8,12,19]. We use complementary bulk/surface techniques to examine the validity of this scenario, and explore the connection between charge ordering and fermiology.By applying a suite of complementary tools to a single cuprate material, Bi 2 Sr 2−x La x CuO 6+δ (Bi2201), we reveal that the charge order in this system emerges just below T * , and that its wavevector corresponds to the Fermi arc tips rather than the antinodal nesting vector. We quantify the Fermi surface using ARPES, and we look for charge modulations along the Cu-O bond directions in both real-and reciprocalspace, using STM and REXS. The single-layer Bi2201 is well suited to this purpose owing to: (i) its two-dimensionality and high degree of crystallinity [22,23], and (ii) the possibility of probing the temperature evolution across T * , which is bettercharacterized [15,16] and more accessible than in bilayer sys-

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.

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.

The electronic structure of simple crystalline solids can be completely described in terms either of local quantum states in real space (r-space), or of wave-like states defined in momentum-space (k-space). However, in the copper oxide superconductors, neither of these descriptions alone may be sufficient. Indeed, comparisons between r-space and k-space studies of Bi2Sr2CaCu2O8+delta (Bi-2212) reveal numerous unexplained phenomena and apparent contradictions. Here, to explore these issues, we report Fourier transform studies of atomic-scale spatial modulations in the Bi-2212 density of states. When analysed as arising from quasiparticle interference, the modulations yield elements of the Fermi-surface and energy gap in agreement with photoemission experiments. The consistency of numerous sets of dispersing modulations with the quasiparticle interference model shows that no additional order parameter is required. We also explore the momentum-space structure of the unoccupied states that are inaccessible to photoemission, and find strong similarities to the structure of the occupied states. The copper oxide quasiparticles therefore apparently exhibit particle-hole mixing similar to that of conventional superconductors. Near the energy gap maximum, the modulations become intense, commensurate with the crystal, and bounded by nanometre-scale domains. Scattering of the antinodal quasiparticles is therefore strongly influenced by nanometre-scale disorder.

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The doping dependence of nanoscale electronic structure in superconducting Bi(2)Sr(2)CaCu(2)O(8 + delta) is studied by scanning tunneling microscopy. At all dopings, the low energy density-of-states modulations are analyzed according to a simple model of quasiparticle interference and found to be consistent with Fermi-arc superconductivity. The superconducting coherence peaks, ubiquitous in near-optimal tunneling spectra, are destroyed with strong underdoping and a new spectral type appears. Exclusively in regions exhibiting this new spectrum, we find local "checkerboard" charge ordering of high energy states, with a wave vector of Q = (+/- 2pi/4.5a(0),0); (0, +/- 2pi/4.5a(0)) +/- 15%. Surprisingly, this spatial ordering of high energy states coexists harmoniously with the low energy Bogoliubov quasiparticle states.

We present an atomic resolution scanning tunneling spectroscopy study of superconducting BaFe1.8Co0.2As2 single crystals in magnetic fields up to 9 T. At zero field, a single gap with coherence peaks at Delta=6.25 meV is observed in the density of states. At 9 and 6 T, we image a disordered vortex lattice, consistent with isotropic, single flux quantum vortices. Vortex locations are uncorrelated with strong-scattering surface impurities, demonstrating bulk pinning. The vortex-induced subgap density of states fits an exponential decay from the vortex center, from which we extract a coherence length xi=27.6+/-2.9 A, corresponding to an upper critical field Hc2=43 T.