Eduardo H. da Silva Neto

Ubiquitous Interplay Between Charge Ordering and High-Temperature Superconductivity in Cuprates

Besides superconductivity, copper-oxide high-temperature superconductors are susceptible to other types of ordering. We used scanning tunneling microscopy and resonant elastic x-ray scattering measurements to establish the formation of charge ordering in the high-temperature superconductor Bi2Sr2CaCu2O8+x. Depending on the hole concentration, the charge ordering in this system occurs with the same period as those found in Y-based or La-based cuprates and displays the analogous competition with superconductivity. These results indicate the similarity of charge organization competing with superconductivity across different families of cuprates. We observed this charge ordering to leave a distinct electron-hole asymmetric signature (and a broad resonance centered at +20 milli–electron volts) in spectroscopic measurements, indicating that it is likely related to the organization of holes in a doped Mott insulator. Surface and bulk measurements in bismuth-based cuprates agree and indicate a short-range charge order. [Also see Perspective by Morr] Copper-Oxide Superconductors Copper-oxide superconductors have a complex electronic structure. A charge density order has been observed in two cuprate families; however, it has been unclear whether such an order exists in Bi-based compounds (see the Perspective by Morr). Comin et al. (p. 390, published online 19 December) and da Silva Neto et al. (p. 393, published online 19 December) address this question in single-layer and double-layer Bibased cuprates, respectively. For both families of materials, surface measurements by scanning tunneling spectroscopy agree with bulk measurements obtained through resonant elastic x-ray scattering, which suggests the formation of short-range correlations that modulate the charge density of the carriers over a range of dopings. Thus, charge ordering may represent a common characteristic of the major cuprate families.

Fluctuating stripes at the onset of the pseudogap in the high-Tc superconductor Bi2Sr2CaCu2O8+x

Doped Mott insulators have a strong propensity to form patterns of holes and spins often referred to as stripes. In copper oxides, doping also gives rise to the pseudogap state, which can be transformed into a high-temperature superconducting state with sufficient doping or by reducing the temperature. A long-standing issue has been the interplay between the pseudogap, which is generic to all hole-doped copper oxide superconductors, and stripes, whose static form occurs in only one family of copper oxides over a narrow range of the phase diagram. Here we report observations of the spatial reorganization of electronic states with the onset of the pseudogap state in the high-temperature superconductor Bi2Sr2CaCu2O8+x, using spectroscopic mapping with a scanning tunnelling microscope. We find that the onset of the pseudogap phase coincides with the appearance of electronic patterns that have the predicted characteristics of fluctuating stripes. As expected, the stripe patterns are strongest when the hole concentration in the CuO2 planes is close to 1/8 (per copper atom). Although they demonstrate that the fluctuating stripes emerge with the onset of the pseudogap state and occur over a large part of the phase diagram, our experiments indicate that the stripes are a consequence of pseudogap behaviour rather than its cause.

Visualizing heavy fermions emerging in a quantum critical Kondo lattice

In solids containing elements with f orbitals, the interaction between f-electron spins and those of itinerant electrons leads to the development of low-energy fermionic excitations with a heavy effective mass. These excitations are fundamental to the appearance of unconventional superconductivity and non-Fermi-liquid behaviour observed in actinide- and lanthanide-based compounds. Here we use spectroscopic mapping with the scanning tunnelling microscope to detect the emergence of heavy excitations with lowering of temperature in a prototypical family of cerium-based heavy-fermion compounds. We demonstrate the sensitivity of the tunnelling process to the composite nature of these heavy quasiparticles, which arises from quantum entanglement of itinerant conduction and f electrons. Scattering and interference of the composite quasiparticles is used to resolve their energy–momentum structure and to extract their mass enhancement, which develops with decreasing temperature. The lifetime of the emergent heavy quasiparticles reveals signatures of enhanced scattering and their spectral lineshape shows evidence of energy–temperature scaling. These findings demonstrate that proximity to a quantum critical point results in critical damping of the emergent heavy excitation of our Kondo lattice system.

Visualizing the formation of the Kondo lattice and the hidden order in URu2Si2

Heavy electronic states originating from the f atomic orbitals underlie a rich variety of quantum phases of matter. We use atomic scale imaging and spectroscopy with the scanning tunneling microscope to examine the novel electronic states that emerge from the uranium f states in URu2Si2. We find that, as the temperature is lowered, partial screening of the f electrons’ spins gives rise to a spatially modulated Kondo–Fano resonance that is maximal between the surface U atoms. At T = 17.5 K, URu2Si2 is known to undergo a second-order phase transition from the Kondo lattice state into a phase with a hidden order parameter. From tunneling spectroscopy, we identify a spatially modulated, bias-asymmetric energy gap with a mean-field temperature dependence that develops in the hidden order state. Spectroscopic imaging further reveals a spatial correlation between the hidden order gap and the Kondo resonance, suggesting that the two phenomena involve the same electronic states.

Visualizing nodal heavy fermion superconductivity in CeCoIn5

By means of low-temperature scanning tunnelling spectroscopy, a heavy fermion material in its superconducting and mixed states can be imaged. Besides probing the superconducting gap symmetry, the measurements also reveal a pseudogap.

Charge ordering in the electron-doped superconductor Nd2–xCexCuO4

Finding order in exotic superconductors Physicists can coax some copper-oxide compounds into becoming superconducting by chemically adding extra charge carriers: holes or electrons. Concentrating on hole-doped materials, researchers have found a host of different phases in the neighborhood of or co-existing with superconductivity. One such phase is a modulation in charge density [a charge density wave (CDW)] that appears to be ubiquitous in hole-doped families. Da Silva Neto et al. now show that a similar phase exists in the electron-doped material Nd2-xCexCuO4. As they cooled the material, the authors first detected the CDW at temperatures considerably higher than in the hole-doped copper-oxides. Science, this issue p. 282 Resonant x-ray scattering is used to detect ordering similar to that observed in hole-doped cuprates. In cuprate high-temperature superconductors, an antiferromagnetic Mott insulating state can be destabilized toward unconventional superconductivity by either hole or electron doping. In hole-doped (p-type) cuprates, a charge ordering (CO) instability competes with superconductivity inside the pseudogap state. We report resonant x-ray scattering measurements that demonstrate the presence of charge ordering in the n-type cuprate Nd2–xCexCuO4 near optimal doping. We find that the CO in Nd2–xCexCuO4 occurs with similar periodicity, and along the same direction, as in p-type cuprates. However, in contrast to the latter, the CO onset in Nd2–xCexCuO4 is higher than the pseudogap temperature, and is in the temperature range where antiferromagnetic fluctuations are first detected. Our discovery opens a parallel path to the study of CO and its relationship to antiferromagnetism and superconductivity.

Doping-dependent charge order correlations in electron-doped cuprates

Resonant x-ray scattering clarifies the link between charge order and magnetism/superconductivity in n-doped cuprates. Understanding the interplay between charge order (CO) and other phenomena (for example, pseudogap, antiferromagnetism, and superconductivity) is one of the central questions in the cuprate high-temperature superconductors. The discovery that similar forms of CO exist in both hole- and electron-doped cuprates opened a path to determine what subset of the CO phenomenology is universal to all the cuprates. We use resonant x-ray scattering to measure the CO correlations in electron-doped cuprates (La2−xCexCuO4 and Nd2−xCexCuO4) and their relationship to antiferromagnetism, pseudogap, and superconductivity. Detailed measurements of Nd2−xCexCuO4 show that CO is present in the x = 0.059 to 0.166 range and that its doping-dependent wave vector is consistent with the separation between straight segments of the Fermi surface. The CO onset temperature is highest between x = 0.106 and 0.166 but decreases at lower doping levels, indicating that it is not tied to the appearance of antiferromagnetic correlations or the pseudogap. Near optimal doping, where the CO wave vector is also consistent with a previously observed phonon anomaly, measurements of the CO below and above the superconducting transition temperature, or in a magnetic field, show that the CO is insensitive to superconductivity. Overall, these findings indicate that, although verified in the electron-doped cuprates, material-dependent details determine whether the CO correlations acquire sufficient strength to compete for the ground state of the cuprates.

Detection of electronic nematicity using scanning tunneling microscopy

Electronic nematic phases have been proposed to occur in various correlated electron systems and were recently claimed to have been detected in scanning tunneling microscopy (STM) conductance maps of the pseudogap states of the cuprate high-temperature superconductor Bi2Sr2CaCu2O8+x (Bi-2212). We investigate the influence of anisotropic STM tip structures on such measurements and establish, with a model calculation, the presence of a tunneling interference effect within an STM junction that induces energy-dependent symmetry-breaking features in the conductance maps. We experimentally confirm this phenomenon on different correlated electron systems, including measurements in the pseudogap state of Bi-2212, showing that the apparent nematic behavior of the imaged crystal lattice is likely not due to nematic order but is related to how a realistic STM tip probes the band structure of a material. We further establish that this interference effect can be used as a sensitive probe of changes in the momentum structure of the samples quasiparticles as a function of energy.

Scattering from incipient stripe order in the high-temperature superconductor Bi 2 Sr 2 CaCu 2 O 8 + δ

Recently, we have used spectroscopic mapping with a scanning tunneling microscope to probe modulations of the electronic density of states in single crystals of the high-temperature superconductor Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8+{delta}} (Bi-2212) as a function of temperature [C.V. Parker et al. Nature (London) 468 677 (2010)]. These measurements showed Cu-O bond-oriented modulations that form below the pseudogap temperature with a temperature-dependent energy dispersion displaying different behaviors in the superconducting and pseudogap states. Here we demonstrate that quasiparticle scattering from impurities does not capture the experimentally observed energy and temperature dependence of these modulations. Instead, a model of scattering of quasiparticles from short-range stripe order, with periodicity near four lattice constants (4a), reproduces the experimentally observed energy dispersion of the bond-oriented modulations and its temperature dependence across the superconducting critical temperature T{sub c}. The present study confirms the existence of short-range stripe order in Bi-2212.

Response to Comment on “Broken translational and rotational symmetry via charge stripe order in underdoped YBa2Cu3O6+y”

Fine questions our interpretation of unidirectional stripes over a bidirectional checkerboard and illustrates his criticism by simulating a momentum space structure consistent with our data and corresponding to a checkerboard-looking real space density. Here, we use a local rotational-symmetry analysis to demonstrate that the simulated image is actually composed of locally unidirectional modulations of the charge density, consistent with our original conclusions.