Charge ordering in the electron-doped superconductor Nd2–xCexCuO4

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Science  16 Jan 2015:
Vol. 347, Issue 6219, pp. 282-285
DOI: 10.1126/science.1256441

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


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.

Copper oxide superconductors are susceptible to a number of instabilities, but the relevance of these phases to the superconducting pairing mechanism is unclear. Charge ordering (CO) has emerged as a universal feature of hole-doped (p-type) cuprates, but it has so far not been detected in n-type cuprates (1) (Fig. 1A). Early evidence for a CO in the cuprates came from the detection in La-based cuprates of a periodic organization of spins and charge known as stripes (25), where the charge is periodic every four lattice constants along the Cu-O bond direction. More recently, following evidence for Fermi surface reconstruction from quantum oscillations (6, 7), nuclear magnetic resonance (8) and x-ray scattering measurements (9, 10) have directly shown the presence of a similar CO competing with superconductivity in Y-based cuprates. The opportunity to directly probe CO in reciprocal space has further propelled several resonant x-ray scattering measurements of the Y-based family (1113) as well as the detection of CO in Bi cuprates (1416)—substantiating earlier surface evidence by scanning tunneling microscopy (1720)—and also in the single-layer Hg compound (21).

Fig. 1 Charge ordering in electron-doped cuprates.

(A) Temperature-doping phase diagram for the cuprates, including the AF parent state (green), the superconductivity (SC, blue), and distinct n-type (faded green) and p-type (gray) pseudogap phases. The CO phase observed in p-type cuprates is marked in red. (B) The Cu-L3 absorption edge at 931.5 eV (2p → 3d transition) and a schematic of the scattering geometry. (C and D) On- and off-resonance θ scans at 22 K, showing the RXS diffraction signal as a function of in-plane momentum transfer (H) along the Cu-O bond direction [see (B)] for x = 0.14 and x = 0.15, respectively. To provide a better comparison, the off-resonance scans were rescaled to match the tails of the on-resonance θ scans. The yellow stars mark the H values of highest intensity for the two samples (obtained from Fig. 3).

Studies of Bi-based cuprates, for which a considerable amount of angle-resolved photoemission spectroscopy (ARPES) data are available, show that the CO wave vector connects the ends of the Fermi arcs (14, 15)—an observation that links the existence of CO to the pseudogap in hole-doped systems. Additionally, doping-dependent measurements on bilayer systems (9, 13, 22, 23) find charge ordering to be most pronounced in a region of hole doping near x = 1/8, where stripes are predominant in La-based cuprates (2, 3). These results raise the questions of whether the particular phenomenology of the hole-doped cuprates such as the pseudogap-induced Fermi arcs, or the propensity toward stripe formation, are necessary ingredients for CO formation, or whether CO is a generic electronic property of the CuO2 layer that is ubiquitous to all cuprates including n-type materials.

Here, we report resonant x-ray scattering (RXS) measurements on the electron-doped cuprate superconductor Nd2–xCexCuO4 (24). Our studies were performed on samples with doping levels (x = 0.14 ± 0.01 and x = 0.15 ± 0.01) for which quantum oscillations indicate a small Fermi surface (25, 26). We use the standard scattering geometry (Fig. 1B) (24), similar to previous studies (9, 14, 15). The tetragonal b axis of the sample is positioned perpendicular to the scattering plane, allowing the in-plane components of momentum transfer to be accessed by rotating the sample around the b axis (θ scan). For RXS measurements, the energy of the incoming photons is fixed to the maximum of the Cu-L3 absorption edge, which is at E ≈ 931.5 eV (Fig. 1B).

Our main finding is summarized in Fig. 1, C and D. An RXS peak is observed at an in-plane momentum transfer of H ≈ –0.24 rlu (reciprocal lattice units) along the Cu-O bond direction; this is notably similar in periodicity and direction to the x-ray scattering peaks found in the hole-doped materials (35, 916, 21, 23). The use of photons tuned to the Cu-L3 edge is expected to greatly enhance the sensitivity in our measurement to charge modulations involving the valence electrons in the CuO2 planes (3). As the photon energy is tuned away from resonance, the distinct peak near H = –0.24 disappears, thus confirming its electronic origin (Fig. 1, C and D) (24). This shows the presence of charge ordering in an electron-doped cuprate.

Further insights into charge ordering formation are obtained by temperature-dependent measurements. The distinct CO peak observed at low temperatures (Fig. 2, A and B) weakens as the temperature is raised, but disappears only above 300 K. Although a temperature evolution is clearly seen in the raw data (Fig. 2, A and B, and fig. S3), the small size of the peak relative to the high-temperature background precludes a precise determination of an onset temperature. Nonetheless, within the detection limits of the experiment, the CO seems to gradually develop with lowering of temperature starting around 340 K (Fig. 2C). Note that this temperature is much higher than the pseudogap onset in Nd2–xCexCuO4 [~80 to 170 K in the x = 0.14 to 0.15 doping range (1, 27, 28)], in clear contrast to observations in hole-doped cuprates, where the p-type pseudogap either precedes or matches the emergence of CO (915, 2123). This dichotomy is not completely unexpected given that the pseudogaps observed in p- and n-type cuprates are dissimilar in many ways (1). In particular, the n-type pseudogap has been associated with the buildup of antiferromagnetic (AF) correlations that first appear below 320 K (for x = 0.145 samples), as determined by inelastic neutron scattering measurements (2729). Interestingly, the temperature evolution of the CO resembles the soft onset of AF correlations (28)—an observation that suggests a connection between CO and AF fluctuations in electron-doped cuprates.

Fig. 2 Temperature dependence of the CO.

(A and B) On-resonance θ scans for x = 0.14 and x = 0.15 samples, respectively, at select temperatures, showing that the onset of the charge ordering occurs above 300 K. (C) Temperature dependence of the RXS intensity for the two samples in (A) and (B) obtained from the maxima of the background-subtracted peaks. The intensity in (C) is normalized to the maximum value between the two samples; the error bars represent the standard errors from Lorentzian fits to the background-subtracted peaks (24).

We now use the available knowledge of the Fermi surface of Nd2–xCexCuO4 to further investigate the connection between AF and CO formation. We find that the CO peak, although broad, is centered around an in-plane momentum transfer QCO = 0.23 ± 0.04 and QCO = 0.24 ± 0.04 for x = 0.14 and x = 0.15, respectively (Fig. 3, A and B). Comparison of QCO to the Fermi surface topology measured by ARPES (Fig. 3C, left panel) shows that its value is consistent with scattering between the parallel segments near (π, 0). Thanks to the relative robustness of the AF phase in n-type cuprates, the Fermi surface has often been interpreted to undergo (π, π) folding along the AF zone boundary—a scenario that is consistent with both ARPES (30) and quantum oscillation results (25). In this context, QCO would connect opposite sides of electron pockets centered at (π, 0) (Fig. 3C, right panel). Alternatively, QCO might instead connect the intersections between the AF zone boundary and the underlying Fermi surface, the so-called hot spots where the effect of AF scattering and the pseudogap are maximal (30). However, the conventional expectation that the onset of CO above room temperature should gap the Fermi surface seems to contradict both scenarios, because the pseudogap opens only at the hot spots below 180 K, whereas no gapping is observed near (π, 0) above the superconducting transition (1); this suggests that Fermi surface nesting might not be the origin of the CO. Unfortunately, however, this kind of comparison between temperature scales might be rendered inconclusive by the possibility that the CO never becomes sufficiently long-ranged, or large enough in amplitude, to induce a detectable reconstruction of the Fermi surface (at least in the absence of an applied magnetic field). Indeed, the widths of the CO peaks shown in Fig. 3, A and B, indicate a short correlation length (15 to 27 Å) (24), again similar to what has been observed in Bi-based cuprates (1416). Perhaps further measurements, spanning larger doping ranges, will be able to test exactly which momentum states are involved in the CO, although the broadness of the CO peak in reciprocal space might ultimately limit the precision to which the location of QCO on the Fermi surface can be determined.

Fig. 3 Electronic origin of the CO.

(A and B) CO peak extracted by subtraction of the highest-temperature θ scan from an average of the lowest-temperature θ scans (22 to 180 K) (24). A fit of the data to a Lorentzian plus linear background function (red line) is used to indicate the H value of highest intensity, which is –0.23 ± 0.04 rlu for the x = 0.14 sample (A) and –0.24 ± 0.04 rlu for the x = 0.15 sample (B). The extracted peaks in (A) and (B) are normalized to their respective maxima. (C) Fermi surface of Nd2–xCexCuO4 (x = 0.15) measured by ARPES (30) (left) and a schematic of the expected Fermi surface reconstruction (right) due to AF folding (yellow diamond). The folded Fermi surface is composed of hole (red) and electron (cyan) pockets. The arrows (white and black) and dashed lines represent QCO = 0.24 rlu, and connect either the parallel segments of the Fermi surface near (π, 0) or the intersection with the AF zone boundary.

The fact that CO never develops into a long-ranged electronic ground state might also hinder the ability of transport or thermodynamic probes to detect it. However, we find that the presence of CO might be relevant to the interpretation of experiments that probe the inelastic excitations of Nd2–xCexCuO4. We start by observing that the value of QCO is consistent with the phonon anomaly near H ≈ 0.2 observed by inelastic x-ray scattering in Nd2–xCexCuO4 (31). More recently, Hinton et al. (32) reported time-resolved reflectivity studies that show the presence of a fluctuating order competing with superconductivity, although they could not determine which electronic degrees of freedom (i.e., charge or spin) were responsible for such order. Additionally, resonant inelastic x-ray scattering measurements (33, 34) have recently shown the presence of an inelastic mode—above a minimum energy transfer of 300 ± 30 meV [comparable to the pseudogap (30)]—which is distinct from the well-characterized AF fluctuations reminiscent of the Mott-insulating parent state (28, 3335). Whereas Ishii et al. (34) ascribed this new mode to particle-hole charge excitations, Lee et al. (33) proposed that the mode might be the consequence of an unspecified broken symmetry—a scenario supported by their observation that this mode disappears above 270 K for x = 0.166. Our discovery of charge ordering in Nd2–xCexCuO4 might provide the missing piece of information to interpret the aforementioned studies by identifying the actual broken symmetry.

Finally, on a fundamental level, some degree of electron-hole asymmetry should be expected in the cuprate phase diagram. In fact, whereas doped hole states below the charge transfer gap have a strong O-2p character, n-type doping creates low-energy electronic states of predominantly Cu-3d character in the upper Hubbard band (3638). This dichotomy, together with recent RXS reports of a bond-centered CO in p-type materials (39), suggests that the n-type CO observed here may instead be centered on the Cu sites—an idea that requires further investigation. However, despite this underlying electron-hole asymmetry, the CO uncovered in Nd2–xCexCuO4 by our study shows several similarities to its p-type equivalent, such as its direction, periodicity, and short correlation length (14, 15). In addition, our observation of a connection between the onset of CO and AF fluctuations suggests that the latter might generally lead to an accompanying intertwined charge order in unconventional superconductors, regardless of which orbitals are involved in the CO (40, 41). If such is the case, detailed studies will be necessary to understand the role of antiferromagnetism in charge order formation, perhaps even beyond the cuprates. Nonetheless, our discovery of charge ordering in n-type cuprates expands the universality of this phenomenon to the electron-doped side of the phase diagram, and provides a new avenue to understand its microscopic origin by exploiting the differences between p- and n-type cuprates.

Supplementary Materials

Materials and Methods

Supplementary Text

Figs. S1 to S4

Reference (42)

References and Notes

  1. See supplementary materials on Science Online.
  2. Acknowledgments: We thank J. Shin for the wavelength dispersive x-ray (WDX) measurements, S. Saha for the susceptibility measurements, and N. P. Armitage, S. A. Kivelson, P. A. Lee, and A.-M. S. Tremblay for fruitful discussions. Supported by the Canadian Institute for Advanced Research (CIFAR) Global Academy (E.H.d.S.N.); the Canadian Light Source Graduate Student Travel Support Program (R.C.); the Max Planck–University of British Columbia Centre for Quantum Materials, the Killam, Alfred P. Sloan, Alexander von Humboldt, and NSERC’s Steacie Memorial Fellowships (A.D.); the Canada Research Chairs Program (A.D. and G.A.S.); and the Natural Sciences and Engineering Research Council of Canada (NSERC), Canada Foundation for Innovation (CFI), and CIFAR Quantum Materials. Work at the University of Maryland was supported by NSF grant DMR 1104256. All of the x-ray experiments were performed at beamline REIXS of the Canadian Light Source, which is funded by CFI, NSERC, National Research Council Canada, Canadian Institutes of Health Research, the Government of Saskatchewan, Western Economic Diversification Canada, and the University of Saskatchewan.
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