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 Bi2Sr2CaCu2O(8+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.

Charge-ordered ground states permeate the phenomenology of 3d-based transition metal oxides, and more generally represent a distinctive hallmark of stronglycorrelated states of matter. The recent discovery of charge order in various cuprate families fueled new interest into the role played by this incipient broken symmetry within the complex phase diagram of high-T c superconductors.Here we use resonant X-ray scattering to resolve the main characteristics of the charge-modulated state in two cuprate families: Bi 2 Sr 2−x La x CuO 6+δ (Bi2201) and YBa 2 Cu 3 O 6+y (YBCO). We detect no signatures of spatial modulations along the nodal direction in Bi2201, thus clarifying the inter-unit-cell momentum-structure of charge order. We also resolve the intra-unit-cell symmetry of the charge ordered state, which is revealed to be best represented by a bond-order with modulated charges on the O-2p orbitals and a prominent d-wave character. These results provide insights on the microscopic description of charge order in cuprates, and on its origin and interplay with superconductivity.Complex oxides exhibit a mosaic of exotic electronic phases with various symmetry-broken ground states that revolve around three main instabilities: antiferromagnetism, charge order, and superconductivity. In particular, charge order -the tendency of the valence electrons to segregate into periodically-modulated structures -is found in various classes of strongly-correlated 3d-oxides, such as manganites [1], nickelates [2], and cobaltates [3]. The original discovery of period-4 stripe-like charge correlations in the La-based materials [4][5][6][7] confirmed the central role played by chargeordered states in the physics of underdoped cuprates, as anticipated by earlier theoretical work [8][9][10][11][12]. Following further indications by surface-sensitive scanning tunnelling microscopy (STM) [13, 14], the field was recently revived by the detection of charge-modulated states in YBCO using nuclear magnetic resonance [15] and resonant X-ray scattering (RXS), with wavevector Q * ∼ 0.31 reciprocal lattice units (r.l.u., used hereafter) [16][17][18][19][20][21]. Even more recently, this phenomenology was confirmed in Bi-based materials (with Q * ∼ 0.26 and 0.3 in single-and double-layer compounds, respectively), following observations in both bulk/momentum space (with RXS) FIG. 1:Charge ordering patterns and wavevectors. a, Schematics of a RXS experiment. b, Low-temperature RXS (at photon energy hν = 931.5 eV) from an underdoped Bi2201-UD15K sample, mapping reciprocal-space features along the two high-symmetry directions: (H, 0), antinodal, green (reproduced from Ref. 22, the full line represents a Gaussian fit plus background); and (H, H), nodal, orange. c,e, Modulation of the charge density ∆ρ(x, y), with functional form given by a sum (c) and product (e) of cosines, and a wavevector magnitude Q * = 0.265 r.l.u. (black bars indicate the period and direction of the spatial modulation, expressed in terms of the lattice parameter a = 3.86Å). The blu...

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 URu 2 Si 2 . 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 ¼ 17.5 K, URu 2 Si 2 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.heavy fermion | scanning tunneling spectroscopy A remarkable variety of collective electronic phenomena have been discovered in compounds with partially filled f orbitals, where electronic excitations act as heavy fermions (1, 2). Like other correlated electronic systems, such as the high temperature superconducting cuprates, several of the heavy fermion compounds display an interplay between magnetism and superconductivity and have a propensity toward superconducting pairing with unconventional symmetry (1-5). However, unlike cuprates, or the newly discovered ferropnictides, the heavy fermion systems do not suffer from inherent dopant-induced disorder and offer a clean material system for the study of correlated electrons. The local f electrons interact both with the itinerant spd electrons as well as with each other, resulting in a rich variety of electronic phases. In many of these materials, screening of the local moments by the Kondo effect begins at relatively high temperatures resulting in a heavy fermion state at low temperatures. Exchange interactions between the local moments become more important at lower temperatures and can result in the formation of magnetic phases as well as superconductivity at even lower temperatures. Among the heavy fermion compounds perhaps the most enigmatic is the URu 2 Si 2 system, which undergoes a second-order phase transition with a rather large change in entropy (6-8) at 17.5 K from a paramagnetic phase with Kondo screening to a phase with an unknown order parameter (9). This material possesses low-energy commensurate and incommensurate spin excitations, which are gapped below the hidden order (HO) transition temperature (10-13). These features are believed to be signatures of a more complex order parameter, the identification of which has so far not been possible despite numerous investigations (12-18). Moreover, analogous to other correlated systems, this unusual conducting phase is transformed into an unconventional superconducting state at 1.5 K (6,8,19), the understanding of which hinges on fo...

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Understanding the origin of superconductivity in strongly correlated electron systems continues to be at the forefront of the unsolved problems of physics 1 . Among the heavy f-electron systems, CeCoIn 5 is one of the most fascinating, as it shares many of the characteristics of correlated d-electron high-T c cuprate and pnictide superconductors 2-4 , including competition between antiferromagnetism and superconductivity 5 . Although there has been evidence for unconventional pairing in this compound 6-11 , high-resolution spectroscopic measurements of the superconducting state have been lacking. Previously, we have used high-resolution scanning tunnelling microscopy (STM) techniques to visualize the emergence of heavy fermion excitations in CeCoIn 5 and demonstrate the composite nature of these excitations well above T c (ref. 12). Here we extend these techniques to much lower temperatures to investigate how superconductivity develops within a strongly correlated band of composite excitations. We find the spectrum of heavy excitations to be strongly modified just before the onset of superconductivity by a suppression of the spectral weight near the Fermi energy (E F ), reminiscent of the pseudogap state 13,14 in the cuprates. By measuring the response of superconductivity to various perturbations, through both quasiparticle interference (QPI) and local pair-breaking experiments, we demonstrate the nodal d-wave character of superconducting pairing in CeCoIn 5 .CeCoIn 5 undergoes a superconducting transition at 2.3 K. Despite evidence of unconventional pairing, consensus on the mechanism of pairing and direct experimental verification of the order parameter symmetry are still lacking [6][7][8][9]11 . Moreover, experiments have suggested that superconductivity in this compound emerges from a state of unconventional quasiparticle excitations with a pseudogap phase similar to that found in underdoped high-T c cuprates [15][16][17] . Previously, we demonstrated that scanning tunnelling spectroscopic techniques can be used to directly visualize the emergence of heavy fermion excitations in CeCoIn 5 and their quantum critical nature 12 . Through these measurements, we also demonstrated the composite nature of heavy quasiparticles and showed their band formation as the f -electrons hybridize with the spd-electrons starting at 70 K, well above T c (ref. 12). This previous breakthrough, together with our recent development of high-resolution millikelvin STM, offers a unique opportunity to measure how superconductivity emerges in a heavy electron system. Figure 1 shows STM topographs of the two commonly observed atomically ordered surfaces of CeCoIn 5 produced after the cleaving of single crystals in situ in the ultra-high vacuum environment 1 Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, New Jersey 08544, USA, 2 Condensed Matter and Magnet Science, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA. † These authors contributed equally to this work. *e-mail: yazdani@pr...

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 Nd(2-x)Ce(x)CuO4 near optimal doping. We find that the CO in Nd(2-x)Ce(x)CuO4 occurs with similar periodicity, and along the same direction, as in p-type cuprates. However, in contrast to the latter, the CO onset in Nd(2-x)Ce(x)CuO4 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.

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.Comment: preprint version, 26 pages, 6 figures. Supplementary: 15 pages, 14 figure

Following the early discovery of stripe-like order in La-based copper-oxide superconductors, charge ordering instabilities were observed in all cuprate families. However, it has proven difficult to distinguish between uni-(stripes) and bi-directional (checkerboard) charge order in Y-and Bi-based materials.Here we use resonant x-ray scattering (RXS) to measure the two-dimensional structure factor in YBa 2 Cu 3 O 6+y , in reciprocal space. Our data reveal the presence of charge stripe order, i.e. locally unidirectional density waves, suggesting it as the true microscopic nature of charge modulations in cuprates. At the same time, we find that the well-established competition between charge order and superconductivity is stronger for charge correlations across than along the stripes, which provides additional evidence for the intrinsic unidirectional nature of the charge order.Recent studies of Y-based copper oxides have highlighted the importance of a chargeordered electronic ground state, also termed charge-density-wave (CDW), as a central element within the phenomenology of high-temperature superconductors (1-14). The family of YBa 2 Cu 3 O 6+y (YBCO) compounds have yielded a wealth of experimental results that enabled advancements in our understanding of CDW instabilities and their interplay with superconductivity (9)(10)(11)(15)(16)(17)(18)(19)(20)(21)(22).YBCO is a layered copper-oxide-based material where hole doping is controlled by the oxygen stoichiometry in the chain layer -characterized by uniaxial CuO chains running along the crystallographic b axis. In addition to ordering within the chain layer -attained via the periodic alternation of fully-oxygenated and fully-depleted CuO chains -recent experiments have extensively shown the presence of charge ordering in the CuO 2 planes, with an incommensurate wavevector Q ∼ 0.31 reciprocal lattice units (23), corresponding to a period of approximately 3 unit cells in real space (9)(10)(11). Although the stripy nature of La-based cuprates has been long 2 established (1-3), the local symmetry of the CDW in YBCO has not yet been resolved as both charge stripes (in the presence of 90• rotated domains)and checkerboard are consistent with the globally bidirectional structure of the CDW -characterized by wavevectors along both the a and b axes, at Q a ∼ (0.31, 0) and Q b ∼ (0, 0.31), respectively (10,11,(24)(25)(26). This leaves open the fundamental question as to whether stripes are the underlying charge instability in the whole class of hole-doped cuprates.Here we study the local density correlations of the charge-ordered state, and the interaction of the latter with superconductivity (SC) in underdoped YBCO, using resonant x-ray scattering (RXS). This technique, which is now at full maturity, represents a unique combination of diffraction (to probe reciprocal space) and resonant absorption (allowing element-specificity and therefore site-selectivity), and directly measures the structure factor S(Q x , Q y ), where Q x and Q y represent the momenta along the recipro...