Atomic-scale images of charge ordering in a mixed-valence manganite

Transition-metal perovskite oxides exhibit a wide range of extraordinary but imperfectly understood phenomena. Charge, spin, orbital, and lattice degrees of freedom all undergo order-disorder transitions in regimes not far from where the best-known of these phenomena, namely high-temperature superconductivity of the copper oxides, and the 'colossal' magnetoresistance of the manganese oxides, occur. Mostly diffraction techniques, sensitive either to the spin or the ionic core, have been used to measure the order. Unfortunately, because they are only weakly sensitive to valence electrons and yield superposition of signals from distinct mesoscopic phases, they cannot directly image mesoscopic phase coexistence and charge ordering, two key features of the manganites. Here we describe the first experiment to image charge ordering and phase separation in real space with atomic-scale resolution in a transition metal oxide. Our scanning tunneling microscopy (STM) data show that charge order is correlated with structural order, as well as with whether the material is locally metallic or insulating, thus giving an atomic-scale basis for descriptions of the manganites as mixtures of electronically and structurally distinct phases.Comment: 8 pages, 4 figures, 19 reference

Local edge modes in doped cuprates with checkerboard polaronic heterogeneity

We study a periodic polaronic system, which exhibits a nanoscale superlattice structure, as a model for hole-doped cuprates with checkerboard-like heterogeneity, as has been observed recently by scanning tunneling microscopy (STM). Within this model, the electronic and phononic excitations are investigated by applying an unrestricted Hartree-Fock and a random phase approximation (RPA) to a multiband Peierls-Hubbard Hamiltonian in two dimensions

Power spectrum of many impurities in a d-wave superconductor

Recently the structure of the measured local density of states power spectrum of a small area of the \BSCCO (BSCCO) surface has been interpreted in terms of peaks at an "octet" of scattering wave vectors determined assuming weak, noninterfering scattering centers. Using analytical arguments and numerical solutions of the Bogoliubov-de Gennes equations, we discuss how the interference between many impurities in a d-wave superconductor alters this scenario. We propose that the peaks observed in the power spectrum are not the features identified in the simpler analyses, but rather "background" structures which disperse along with the octet vectors. We further consider how our results constrain the form of the actual disorder potential found in this material.Comment: 5 pages.2 figure

Theory of the Diamagnetism Above the Critical Temperature for Cuprates

Recently experiments on high critical temperature superconductors has shown that the doping levels and the superconducting gap are usually not uniform properties but strongly dependent on their positions inside a given sample. Local superconducting regions develop at the pseudogap temperature ($T^*$) and upon cooling, grow continuously. As one of the consequences a large diamagnetic signal above the critical temperature ($T_c$) has been measured by different groups. Here we apply a critical-state model for the magnetic response to the local superconducting domains between $T^*$ and $T_c$ and show that the resulting diamagnetic signal is in agreement with the experimental results.Comment: published versio

Muon-spin rotation and magnetization studies of chemical and hydrostatic pressure effects in EuFe_{2}(As_{1-x}P_{x})_{2}

The magnetic phase diagram of EuFe$_{2}$(As$_{1-x}$P$_{x}$)$_{2}$ was investigated by means of magnetization and muon-spin rotation studies as a function of chemical (isovalent substitution of As by P) and hydrostatic pressure. The magnetic phase diagrams of the magnetic ordering of the Eu and Fe spins with respect to P content and hydrostatic pressure are determined and discussed. The present investigations reveal that the magnetic coupling between the Eu and the Fe sublattices strongly depends on chemical and hydrostatic pressure. It is found that chemical and hydrostatic pressure have a similar effect on the Eu and Fe magnetic order.Comment: 11 pages, 10 figure

Inhomogeneous d-wave superconducting state of a doped Mott insulator

Recent scanning tunneling microscope (STM) measurements discovered remarkable electronic inhomogeneity, i.e. nano-scale spatial variations of the local density of states (LDOS) and the superconducting energy gap, in the high-Tc superconductor BSCCO. Based on the experimental findings we conjectured that the inhomogeneity arises from variations in local oxygen doping level and may be generic of doped Mott insulators which behave rather unconventionally in screening the dopant ionic potentials at atomic scales comparable to the short coherence length. Here, we provide theoretical support for this picture. We study a doped Mott insulator within a generalized t-J model, where doping is accompanied by ionic Coulomb potentials centered in the BiO plane. We calculate the LDOS spectrum, the integrated LDOS, and the local superconducting gap, make detailed comparisons to experiments, and find remarkable agreement with the experimental data. We emphasize the unconventional screening in a doped Mott insulator and show that nonlinear screening dominates at nano-meter scales which is the origin of the electronic inhomogeneity. It leads to strong inhomogeneous redistribution of the local hole density and promotes the notion of a local doping concentration. We find that the inhomogeneity structure manifests itself at all energy scales in the STM tunneling differential conductance, and elucidate the similarity and the differences between the data obtained in the constant tunneling current mode and the same data normalized to reflect constant tip-to-sample distance. We also discuss the underdoped case where nonlinear screening of the ionic potential turns the spatial electronic structure into a percolative mixture of patches with smaller pairing gaps embedded in a background with larger gaps to single particle excitations.Comment: 19 pages, final versio

Imaging the Two Gaps of the High-TC Superconductor Pb-Bi2Sr2CuO6+x

The nature of the pseudogap state, observed above the superconducting transition temperature TC in many high temperature superconductors, is the center of much debate. Recently, this discussion has focused on the number of energy gaps in these materials. Some experiments indicate a single energy gap, implying that the pseudogap is a precursor state. Others indicate two, suggesting that it is a competing or coexisting phase. Here we report on temperature dependent scanning tunneling spectroscopy of Pb-Bi2Sr2CuO6+x. We have found a new, narrow, homogeneous gap that vanishes near TC, superimposed on the typically observed, inhomogeneous, broad gap, which is only weakly temperature dependent. These results not only support the two gap picture, but also explain previously troubling differences between scanning tunneling microscopy and other experimental measurements.Comment: 6 page

Dispersive charge density wave excitations and temperature dependent commensuration in Bi2Sr2CaCu2O8+{\delta}

Experimental evidence on high-Tc cuprates reveals ubiquitous charge density wave (CDW) modulations, which coexist with superconductivity. Although the CDW had been predicted by theory, important questions remain about the extent to which the CDW influences lattice and charge degrees of freedom and its characteristics as functions of doping and temperature. These questions are intimately connected to the origin of the CDW and its relation to the mysterious cuprate pseudogap. Here, we use ultrahigh resolution resonant inelastic x-ray scattering (RIXS) to reveal new CDW character in underdoped Bi2Sr2CaCu2O8+{\delta} (Bi2212). At low temperature, we observe dispersive excitations from an incommensurate CDW that induces anomalously enhanced phonon intensity, unseen using other techniques. Near the pseudogap temperature T*, the CDW persists, but the associated excitations significantly weaken and the CDW wavevector shifts, becoming nearly commensurate with a periodicity of four lattice constants. The dispersive CDW excitations, phonon anomaly, and temperature dependent commensuration provide a comprehensive momentum space picture of complex CDW behavior and point to a closer relationship with the pseudogap state

Origin of the Pseudogap in High-Temperature Cuprate Superconductors

Cuprate high-temperature superconductors exhibit a pseudogap in the normal state that decreases monotonically with increasing hole doping and closes at x \approx 0.19 holes per planar CuO2 while the superconducting doping range is 0.05 < x < 0.27 with optimal Tc at x \approx 0.16. Using ab initio quantum calculations at the level that leads to accurate band gaps, we found that four-Cu-site plaquettes are created in the vicinity of dopants. At x \approx 0.05 the plaquettes percolate, so that the Cu dx2y2/O p{\sigma} orbitals inside the plaquettes now form a band of states along the percolating swath. This leads to metallic conductivity and below Tc to superconductivity. Plaquettes disconnected from the percolating swath are found to have degenerate states at the Fermi level that split and lead to the pseudogap. The pseudogap can be calculated by simply counting the spatial distribution of isolated plaquettes, leading to an excellent fit to experiment. This provides strong evidence in favor of inhomogeneous plaquettes in cuprates.Comment: 24 pages (4 pages main text plus 20 pages supplement

Fully Gapped Single-Particle Excitations in the Lightly Doped Cuprates

The low-energy excitations of the lightly doped cuprates were studied by angle-resolved photoemission spectroscopy. A finite gap was measured over the entire Brillouin zone, including along the d_{x^2 - y^2} nodal line. This effect was observed to be generic to the normal states of numerous cuprates, including hole-doped La_{2-x}Sr_{x}CuO_{4} and Ca_{2-x}Na_{x}CuO_{2}Cl_{2} and electron-doped Nd_{2-x}Ce_{x}CuO_{4}. In all compounds, the gap appears to close with increasing carrier doping. We consider various scenarios to explain our results, including the possible effects of chemical disorder, electronic inhomogeneity, and a competing phase.Comment: To appear in Phys. Rev.