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.

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.

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 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.

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.

A universal high energy anomaly in the single particle spectral function is reported in three different families of high temperature superconductors by using angle-resolved photoemission spectroscopy. As we follow the dispersing peak of the spectral function from the Fermi energy to the valence band complex, we find dispersion anomalies marked by two distinctive high energy scales, E1 ≈ 0.38 eV and E2 ≈ 0.8 eV. E1 marks the energy above which the dispersion splits into two branches. One is a continuation of the near parabolic dispersion, albeit with reduced spectral weight, and reaches the bottom of the band at the Γ point at ≈ 0.5 eV. The other is given by a peak in the momentum space, nearly independent of energy between E1 and E2. Above E2, a band-like dispersion re-emerges. We conjecture that these two energies mark the disintegration of the low energy quasiparticles into a spinon and holon branch in the high Tc cuprates.Understanding how doped oxygen holes are transported in the environment of antiferromagnetically coupled copper spin is one of the most fundamental problems in the field of high temperature superconductivity. In 1988 Zhang and Rice [1] proposed that the doped holes in the oxygen 2pσ orbitals form singlets with the spins of the neighboring coppers. The resulting charge-e and spin-0 object is called the Zhang-Rice singlet (ZRS). As the ZRS moves through the CuO 2 plane, the copper spins get rearranged. As a result, the ZRS couples very strongly to the antiferromagnetic environment. Remarkably as a consequence of such strong coupling, quasiparticles emerge at low energies. This is evidenced by the sharp nodal quasiparticle peaks seen in angle-resolved photoemission (ARPES) of almost all cuprate compounds [2,3]. In simple physical terms a quasiparticle is a composite object made of a ZRS and a S=1/2 copper spins. It is widely believed that, at sufficiently low temperatures, superconducting pairing occurs between these quasiparticles giving rise to the high temperature superconducting state. Thus a microscopic understanding of the pairing mechanism of high Tc superconductors requires an in-depth understanding of how a ZRS is dressed into a quasiparticle.Here we present the first systematic study of the evolution of the ARPES spectral function from the Fermi level (E F ≡ 0) to the valence band complex (at energy ≈ 1 eV [4]) for three different families of high temperature superconductors. Our results provide a surprising new experimental understanding on the important quasiparticle formation process discussed above. Specifically, by covering a much broader energy range than typically studied [2], we have identified anomalies in the ARPES spectra occurring at two universal high energy scales, E 1 ≈ 0.38 eV and E 2 ≈ 0.8 eV from E F . We conjecture that these two energies mark the threshold for the disintegration of the low-energy quasiparticles at two different binding levels.ARPES data have been collected at the Advanced Light Source, beamlines 7.0.1, 10.0.1 and 12.0.1. for three different familie...

A complete knowledge of its excitation spectrum could greatly benefit efforts to understand the unusual form of superconductivity occurring in the lightly holedoped copper-oxides. Here we use tunnelling spectroscopy to measure the T→0 spectrum of electronic excitations N(E) over a wide range of hole-density p in superconducting Bi 2 Sr 2 CaCu 2 O 8+δ . We introduce a parameterization for N(E) based upon an anisotropic energy-gap ( ) ( ) 2 / ) ( ) ( 1 y x k Cos k Cos k − Δ = Δ r plus an effective scattering rate which varies linearly with energy E E α = Γ ) ( 2 . We demonstrate that this form of N(E) allows successful fitting of differential tunnelling conductance spectra throughout much of the Bi 2 Sr 2 CaCu 2 O 8+δ phase diagram. The resulting average Δ 1 values rise with falling p along the familiar trajectory of excitations to the 'pseudogap' energy, while the key scattering rate ) ( 1 2 * 2 Δ = Γ = Γ Eincreases from below ~1meV to a value approaching 25meV as the system is underdoped from 2 p~16% to p<10%. Thus, a single, particle-hole symmetric, anisotropic energy-gap, in combination with a strongly energy and doping dependent effective scattering rate, can describe the spectra without recourse to another ordered state.Nevertheless we also observe two distinct and diverging energy scales in the system: the energy-gap maximum Δ 1 and a lower energy scale Δ 0 separating the spatially homogeneous and heterogeneous electronic structures.Hole-doped copper-oxides have their highest superconducting critical temperature T c at hole-densities per CuO 2 of p~16%, and the superconductive state exhibits d-wave symmetry. By measuring STM tip-sample differential conductance dI/dV(r,V) ≡ g(r,V) at each location r and bias voltage V one can achieve energy resolved images of the localdensity-of-excitations N(E) because g(r,V) ∝ N(r,E=eV) (when the N(E) integrated to the junction formation bias is homogeneous 1 ). Near optimal doping, the g(V) spectra appear highly consistent with the theoretical N(E) of a d-wave superconductor; when superconductivity is suppressed by unitary scattering at a Zn atom 2,3 or at the center of a vortex core 3,4 , the two particle-hole symmetric peaks in g(V) are also suppressed as expected of the superconducting coherence peaks. Thus there can be little doubt that the measured N(E) near optimal doping is that of the d-wave superconducting state. But as p is reduced, the electronic excitations begin to exhibit 5,6,7 a 'pseudo' gap (PG) . This is a momentum-space anisotropic energy gap 5-9 in the excitation spectrum whose effects can be detected by numerous spectroscopic and thermodynamic techniques 6,7 far above the superconducting T c (which diminishes to zero as p→0). The PG energy scale increases linearly with diminishing p.Possible explanations for the PG include, for example, effects of hole-doping an antiferromagnetic Mott insulator 10 -14 . Different models for this situation yield an anisotropic energy-gap whose maximum diminishes linearly with increasing p (heuristically, one can view thi...