Progress and perspectives on electron-doped cuprates

Although the vast majority of high-$T_c$ cuprate superconductors are hole-doped, a small family of electron-doped compounds exists. Underinvestigated until recently, there has been tremendous recent progress in their characterization. A consistent view is being reached on a number of formerly contentious issues, such as their order-parameter symmetry, phase diagram, and normal-state electronic structure. Many other aspects have been revealed exhibiting both their similarities and differences with the hole-doped compounds. This review summarizes the current experimental status of these materials. This information is synthesized into a consistent view on a number of topics important to both this material class and the overall cuprate phenomenology including the phase diagram, the superconducting order-parameter symmetry, electron-phonon coupling, phase separation, the nature of the normal state, the role of competing orders, the spin-density wave mean-field description of the normal state, and pseudogap effects.

Figure 1

(Color online) Comparison of the crystal structures of the electron-doped cuprate $R_{2-x}{\mathrm{Ce}}_x\mathrm{Cu}{\mathrm{O}}_4$ and of its closest hole-doped counterpart ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x\mathrm{Cu}{\mathrm{O}}_4$. Here $R$ is one of a number of rare-earth ions, including Nd, Pr, Sm, or Eu. One should note the different directions for the in-plane lattice parameters with respect to the Cu-O bonds.

Figure 2

(Color online) Joint phase diagram of the LSCO/NCCO material systems. The uncertainty regarding the extent of AF on the electron-doped side and its coexistence with superconductivity is shown by the dotted area. Maximum Néel temperatures have been reported as $270\mathrm{K}$ on the electron-doped side in NCO (297), $284\mathrm{K}$ in PCO (449) and $320\mathrm{K}$ on the hole-doped side in LCO (221). $T^{*}$ indicates the approximate extent of the pseudogap (PG) phase. It is not clear if PG phenomena have the same origin on both sides of the phase diagram. At low dopings on the hole-doped side, a spin-glass phase exists (not shown). There is as of yet no evidence for a spin-glass phase in the electron-doped compounds.

Figure 3

Transition temperature $T_c$ as a function of the Ce concentration in reduced NCCO (circles) and PCCO (squares). The closed and open triangles indicate that bulk superconductivity was not observed above $5\mathrm{K}$ for the Nd or Pr systems, respectively. From 456.

Figure 4

Hubbard and charge transfer insulator band structures. (Top) Schematic of the one-band Hubbard model with $U⪢t$. At half filling the chemical potential $\mu$ lies in the middle of the Mott gap. (Middle) Schematic for a charge-transfer band insulator. ${\Delta }_{pd}$ may play the role of an effective Hubbard $U$ with the charge-transfer band (CTB) standing in for the lower Hubbard band. (Bottom) Upon doping the CTB insulator with electrons, the chemical potential $\mu$ presumably moves into the upper Hubbard band.

Figure 5

The highest superconducting onset temperature vs in-plane lattice constant in $T^{\prime }$ structure $R_2{\mathrm{Ce}}_x\mathrm{Cu}{\mathrm{O}}_{4+\delta }$. Note that $T^{\prime }$ phase ${\mathrm{La}}_{2-x}{\mathrm{Ce}}_x\mathrm{Cu}{\mathrm{O}}_{4+\delta }$ can only be stabilized in thin-film form as discussed. From 338.

Figure 6

The lattice parameters of NCCO single crystals and ceramic powders as a function of cerium content $x$ showing the decreasing unit-cell volume with increasing $x$. Solid circles and triangles refer to powder samples and single crystals, respectively. Open circles are the results from 456. From 463.

Figure 7

(Color online) PLCCO phase diagram. (Top) $\delta \text{−}x$ phase diagram of PLCCO (510). (Bottom) Phase diagram for PLCCO as a function of Ce content $x$ (139) as determined by neutron-scattering and SQUID measurements.

Figure 8

Extracted values of $T_c$ for SLCO as a function of doping. Solid and open circles are for the onset and zero resistivity, respectively. From 214.

Figure 9

Phase diagram of the ${\mathrm{Nd}}_2{\mathrm{O}}_3\text{−}\mathrm{Cu}\mathrm{O}$ binary system. Without Ce, the eutectic point corresponds to approximatively 90% CuO content in the flux. From 293.

Figure 10

Equilibrium oxygen partial pressure $p\left({\mathrm{O}}_2\right)$ as a function of oxygen content $y$ for ${\mathrm{Nd}}_{1.85}{\mathrm{Ce}}_{0.15}\mathrm{Cu}{\mathrm{O}}_y$ at $900°\mathrm{C}$. The dashed line indicates the ${\mathrm{Cu}}^{2+}∕{\mathrm{Cu}}^{+}$ transition. Samples below this line are superconducting, while those above are not. From 342.

Figure 11

The phase stability diagram for $x=0.15$ NCCO. The filled diamond symbols are obtained by thermogravimetric analysis and the filled and open circles are compounds which lie within and outside the field of stability, respectively. The filled triangles represent superconducting samples and the open triangles at the bottom represent nonsuperconducting oxides. The dash-dot-dashed line is for the ${\mathrm{Cu}}_2\mathrm{O}\text{−}\mathrm{Cu}\mathrm{O}$ transition and the dotted lines are isocompositions. From 227.

Figure 12

HRTEM images of a reduced ${\mathrm{Nd}}_{1.84}{\mathrm{Ce}}_{0.16}\mathrm{Cu}{\mathrm{O}}_{4+\delta }$ single crystal showing the intercalated layers. The ${(\mathrm{Nd},\mathrm{Ce})}_2{\mathrm{O}}_3$ layers are found to be parallel to the $\mathrm{Cu}{\mathrm{O}}_2$ planes. From 296.

Figure 13

Phase diagram for ${\mathrm{Nd}}_{2-x}{\mathrm{Ce}}_x\mathrm{Cu}{\mathrm{O}}_{4+\delta }$ single crystals as determined by neutron scattering. The Néel temperature is shown as a function of cerium content (x). Full circles: as-grown (oxygenated) samples. Open symbols: reduced samples. Gray circles are the data for the as-grown crystals shifted to simulate the carrier density change with reduction. From 297.

Figure 14

Variation in the transition temperature with the thickness of the PLD films on various substrates. From 301.

Figure 15

(Color online) The transition temperature as a function of cerium doping for $T^{\prime }$ ${\mathrm{La}}_{2-x}{\mathrm{Ce}}_x\mathrm{Cu}{\mathrm{O}}_{4+\delta }$, NCCO, and PCCO thin films grown by MBE. From 241.

Figure 16

(Color online) Cu spin structures for the noncollinear phase of NCO in phase II at $30\mathrm{K}<T<75\mathrm{K}$ or SCO. Nd phases I and III are equivalent to a structure with the central Cu spin of the figure flipped 180° (left). The collinear structure of ${\mathrm{La}}_2\mathrm{Cu}{\mathrm{O}}_4$ (right). The moments (arrows) are aligned along the nearest-neighbor Cu along the Cu-O bonds [(100) and (010)] for $R_2\mathrm{Cu}{\mathrm{O}}_4$ while they point toward the next-nearest neighbor Cu at 45° with respect to the Cu-O bonds [along (110)] for ${\mathrm{La}}_2\mathrm{Cu}{\mathrm{O}}_4$.

Figure 17

(Color online) In-plane Cu spin structures for (a) zero applied magnetic field and a large magnetic field beyond the spin-flop field applied at (b) 45° and (c) 0° with respect to the Cu-O-Cu bonds. (d) In-plane and (e) $c$-axis magnetoresistance of lightly doped ${\mathrm{Pr}}_{1.3}{\mathrm{La}}_{0.7}{\mathrm{Ce}}_x\mathrm{Cu}{\mathrm{O}}_4$ $(x=0.01)$ single crystals at $5\mathrm{K}$ for a magnetic field applied along the (100) or (010) Cu-O bonds and along the (110) Cu-Cu direction. From 256. (f) $c$-axis magnetoresistance at $5\mathrm{K}$ for nonsuperconducting as-grown ${\mathrm{Pr}}_{1.85}{\mathrm{Ce}}_{0.15}\mathrm{Cu}{\mathrm{O}}_4$ as a function of field for three selected in-plane orientations (0°, 15°, and 45°) and (g) as a function of angle at selected magnetic fields below and above the spin-flop field of $5\mathrm{T}$. From 129.

Figure 18

Elastic neutron-scattering intensity as a function of temperature at the ($1∕2$ $1∕2$ 0) reciprocal space position for as-grown ${\mathrm{Nd}}_2\mathrm{Cu}{\mathrm{O}}_4$. The sudden changes in intensity occur at the transition from type I to type II, then type II to type III Nd-Cu moment configurations with decreasing temperature. From 285.

Figure 19

Resistivity of NCCO. (Left) Temperature dependence of the in-plane resistivity of NCCO crystals at various doping levels $x$. (Center) The temperature dependence of the out-of-plane resistivity of NCCO at various doping. (Right) The temperature derivative of the out-of-plane resistivity $(d{\rho }_c∕dT)$. The nominal $T^{*}$ is indicated by the arrow. From 355.

Figure 20

(Color online) The Hall coefficient $R_H$ in ${\mathrm{Pr}}_{2-x}{\mathrm{Ce}}_x\mathrm{Cu}{\mathrm{O}}_4$ films as function of temperature for the various doping levels (top to bottom): $x=0.19$, $x=0.18$, $x=0.17$, $x=0.16$, $x=0.15$, $x=0.14$, $x=0.13$, $x=0.12$, and $x=0.11$ (98).

Figure 21

The Hall coefficient at $0.35\mathrm{K}$ (using the data from Fig. 20). A distinct kink in the Hall coefficient is seen between $x=0.16$ and 0.17. The error on the concentration is approximately 0.003. The error in $R_H$ comes primarily from the error in the film thickness; it is approximately the size of the data points (101).

Figure 22

NCCO Nernst signal. (a) The experimentally measured Nernst signal $e_N$ vs $H$ in optimally doped $x=0.15$ NCCO and $T_c=24.5\mathrm{K}$ from temperatures of $5–30\mathrm{K}$. The dashed lines are fits of the high-field segments to a quasiparticle term of the form $e_N^n(T,H)=c_{1}H+c_3{H}^3$ as detailed in 503. (b) The vortex contribution to the Nernst effect $e_N^s$ as extracted from the data of (a) as also detailed in 503.

Figure 23

Temperature dependence of normal-state Nernst signal at ${\mu }_{0}H=9\mathrm{T}$ for all the doped PCCO films. From 267.

Figure 24

Temperature-dependent resistivity for NCCO $x=0.14$ films damaged with ${\mathrm{He}}^{+}$ ions. From bottom to top, ion fluences are 0, 0.5, 1, 1.5, 2, 2.5, 3, 4, and $4.5\times {10}^{14}\text{ions}∕{\mathrm{cm}}^2$. From 514.

Figure 25

Effect of oxygen content on NCCO. (a) Resistivity as a function of temperature for $x=0.17$ thin films with various oxygen contents. (b) Low-temperature region of the same data. (c) Critical temperature $T_c$ as a function of oxygen content for $x=0.17$ for films grown in oxygen (full circles), solid line is a guide to the eye. Cross, highest $T_c$ under ${\mathrm{N}}_2\mathrm{O}$. Dashed line, schematic of the expected behavior for a carrier driven $T_c$ [see 145]. (d) $T_c$ as a function of the in-plane resistivity at $30\mathrm{K}$. From 145.

Figure 26

Raw data of the directional tunneling measurements for optimally doped NCCO. (a) Temperature dependence of the tunneling spectra measured along the (100) direction. The curves have been shifted for clarity. The temperature increases from the bottom upwards in steps of $1\mathrm{K}$ (from $2\text{to}22\mathrm{K}$) and then $2\mathrm{K}$ (from $22\text{to}30\mathrm{K}$). The thick solid line denotes the data at $26\mathrm{K}$ which is approximately $T_c$. (b) Illustration of the constructed normal conductance background above $T_c$. (c) The normalized $2\mathrm{K}$ spectrum in the (110) direction. From 418.

Figure 27

(Color online) STM tunneling spectra. (a) A $200\mathrm{\AA }$ line cut that shows the variations in coherence peak heights and gap magnitude (Δ). The spectra have been offset for clarity. The gap magnitude, which is defined as half the energy separation between the coherence peaks, varies from $5\text{to}8\mathrm{meV}$ in this line cut. (b) A representative $\pm 100\text{−}\mathrm{mV}$ range $(dI∕dV)$ spectrum that illustrates the dominate V-shaped background. (c) The spectrum in (b) after division by a linear V-shaped function. (d) Additional examples of $dI∕dV$ spectra that demonstrate the clearly resolved coherence peaks and modes resulting from a V-shaped division. From 346.

Figure 28

(Color online) Fermi-surface plot: (a) $x=0.04$, (b) $x=0.10$, and (c) $x=0.15$. EDCs integrated in a $60\mathrm{meV}$ window ($-40\mathrm{meV}$, $+20\mathrm{meV}$) plotted as a function of $\vec{k}$. Data were typically taken in the displayed upper octant and symmetrized across the zone diagonal. Adapted from 33.

Figure 29

(Color online) Doping dependence of the FS in NCCO. (a) Obtained by plotting the ARPES intensity integrated over $\pm 20\mathrm{meV}$ with respect to $E_F$ as a function of momentum. The intensity is normalized to that at $400\mathrm{meV}$ binding energy and symmetrized with respect to the $(0,0)\text{−}(\pi ,\pi )$ direction. (b) Doping dependence of a set of ARPES spectra measured at several $k$ points around the FS at several dopings. From 313.

Figure 30

Temperature dependence of the ARPES spectrum of NCCO $(x=0.13)$ measured in the hot spot (at the position on the Fermi surface shown by a circle in the inset) where the two-component structure is observed clearly. The solid straight lines on the spectra show the linear fits to the high-energy region $(0.2–0.5\mathrm{eV})$ showing that it does not change with temperature. From 314.

Figure 31

(Color online) ARPES intensity within $\pm 30\mathrm{meV}$ of $E_F$ plotted in the BZ quadrant space for nominally $x=0.15$ NCCO, SCCO, and ECCO. White circles show the peak positions of momentum distribution curves (MDCs) at $E_F$, indicating the underlying Fermi surface. Solid curves and dashed curves show the Fermi surface obtained by tight-binding fit to the ARPES data assuming the AFM and paramagnetic band structures, respectively. The FS exhibit significantly less curvature in ECCO as compared to NCCO. Inset: Schematic of the hot spot. Black curve and dashed line represent the Fermi surface and the antiferromagnetic Brillouin-zone boundary, respectively. From 183.

Figure 32

(Color online) Doping dependence of optical conductivity spectra for ${\mathrm{Nd}}_{2-x}{\mathrm{Ce}}_x\mathrm{Cu}{\mathrm{O}}_4$ crystals with $x=0–0.15$ at $10\mathrm{K}$ and a sufficient high temperature $\left(440\mathrm{K}\right)$ for the $x=0.05$ crystal and $290\mathrm{K}$ for the others. From 355.

Figure 33

(Color online) Magnetic Raman response of NCCO. (a) Doping dependence of the $B_{1g}$ two-magnon peak Raman spectra at $20\mathrm{K}$ for crystals of ${\mathrm{Nd}}_{2-x}{\mathrm{Ce}}_x\mathrm{Cu}{\mathrm{O}}_4$. Temperature variation of the $B_{1g}$ Raman spectra for (b) $x=0.05$ and (c) $x=0.10$ crystals. From 355.

Figure 34

Energy spectra of ${\chi }^{″}\left(\omega \right)$ of NCCO obtained from the normal and SC phases $x=0.15$, $T_c=18\mathrm{K}$. From 525.

Figure 35

(Color online) Inelastic neutron scattering on NCCO. (a) Doping dependence of the spin stiffness ${\rho }_s$ normalized to the AF superexchange ($J=125\mathrm{meV}$ for the undoped Mott insulator ${\mathrm{Nd}}_2\mathrm{Cu}{\mathrm{O}}_4$) as $2\pi {\rho }_s∕J$ as well as the low-temperature spin correlation length ${\xi }_0$. The spin stiffness decreases smoothly with doping and reaches zero in an approximately linear fashion around $x_{\mathrm{AF}}\approx 0.134$. The ground state for $x<x_{\mathrm{AF}}$ has long-range AF order as indicated by the diverging ${\xi }_0$. (b) The apparent Néel temperature $T_N$, as determined from elastic scattering, as a function of doping given by the dotted curve. The dashed curve is the extrapolated contour of $\xi ∕a=400$. Adapted from 335.

Figure 36

(Color online) Neutron scattering on PLCCO. (Top) Temperature difference spectrum between 2 and $30\mathrm{K}$ suggests a resonancelike enhancement at $\sim 11\mathrm{meV}$. (Bottom left) Temperature dependence of the neutron intensity $(\sim 1\mathrm{h}$/ point) at $(1∕2,1∕2,0)$ and $10\mathrm{meV}$ in black squares. Diamonds are integrated intensity of the localized signal centered around $Q=(1∕2,1∕2,0)$ above backgrounds. (Bottom right) $Q$ scans at $\omega =10\mathrm{meV}$ above and below the superconducting transitions. From 509.

Figure 37

(Color online) The resonance peak in NCCO. (a) Change in scattering intensity between 4 and $30\mathrm{K}$ at the antiferromagnetic wave vector $(1∕2,1∕2,0)$. (b) Dynamic susceptibility ${\chi }^{″}(Q,\omega )$ which shows two peaks after correcting the measured intensity for the thermal factor. (c) Relative change from $30\text{to}4\mathrm{K}$ in susceptibility at the AF wave vector. (d) Contour plot of ${\chi }^{″}(Q,\omega )$ at $4\mathrm{K}$, made by interpolation of symmetrized momentum scans through the AF zone center with a constant background removed. (e) Local susceptibility in absolute units from the momentum integral of the dynamic susceptibility by comparing with the measured intensity of acoustic phonons. The shaded vertical bands in (a)–(c) indicate the range of values of $2{\Delta }_{\mathrm{el}}$ from Raman scattering (381) corresponding to an estimation of the distribution of gap sizes from chemical inhomogeneity. From 532.

Figure 38

Scaled scattering intensity at $(1∕2,1∕2,0)$ for a superconducting sample of NCCO ($x=0.18$, $T_c=20\mathrm{K}$), plotted as a function of $B∕T$. Field direction is [0,0,1]. Data are compared with the results at $T=5\mathrm{K}$ of 210 ($x=0.15$, $T_c=25\mathrm{K}$). Adapted from 296.

Figure 39

Tunnel-diode driven $LC$ resonator data for three different PCCO single crystals showing power-law behavior of the superfluid density. From 378.

Figure 40

Raman response of superconducting NCCO. (a) Electronic Raman scattering results comparing the response above ($35\mathrm{K}$, dashed line) and below ($11\mathrm{K}$, solid line) the critical temperature in the $B_{1g}$, the $B_{2g}$, and the $A_{1g}$ configurations. (b) A sketch of the position of the hot spots (HS) on the Fermi surface where the gap maximum also occurs. (c) Comparison of the angular dependence of the nonmonotonic $d$-wave gap (solid line) with monotonic $d$-wave (dashed line) and anisotropic $s$-wave gap (dotted line). From 50.

Figure 41

Bottom curves are near $E_F$ ARPES EDCs of optimally doped NCCO from ${\vec{k}}_F$ close to $(\pi ,0.3\pi )$. Open and solid circles are the experimental data at 10 and $30\mathrm{K}$, respectively, while solid lines are fits. Upper curves are the experimental fits without resolution convolution. “Curve No. 2 from Fig. 3” refers to figures given by 30. Upper panel: Gap values extracted from fits at the two $\vec{k}$-space positions using the difference between the 10 and $30\mathrm{K}$ data. Different symbols are for different samples. From 30.

Figure 42

(Color online) Superconducting gap of PLCCO from ARPES. (a) EDCs from ARPES measurements for temperatures above $\left(30\mathrm{K}\right)$ and below $\left(8\mathrm{K}\right)$ the transition temperature for ${\mathrm{Pr}}_{0.89}\mathrm{La}{\mathrm{Ce}}_{0.11}\mathrm{Cu}{\mathrm{O}}_4$ single crystals at three distinct points in $k$ space on the Fermi surface. (b) Leading-edge shift determined as a function of position (angle) on the Fermi surface showing that it fits a nonmonotonic $d$-wave symmetry. From 315.

Figure 43

(Color online) Specific-heat data from 535 on a single crystal of ${\mathrm{Pr}}_{1.85}{\mathrm{Ce}}_{0.15}\mathrm{Cu}{\mathrm{O}}_4$. In (a), the temperature dependence at various magnetic fields is used to extract the linear-$T$ electronic contribution. (b) Field dependence of the linear in $T$ coefficient that shows close to $\sqrt{H}$ dependence in a magnetic field range considerably below $H_{c2}$. The line is a fit by $\gamma \left(H\right)={\gamma }_0+A\sqrt{H}$. These data show also the saturation of the electronic specific heat at roughly $6\mathrm{T}$ interpreted as the bulk upper critical field.

Figure 44

(Color online) Thermal conductivity of PCCO for a heat current in the basal plane. (Top) Plotted as $\kappa ∕T$ vs $T^2$, at different values of the magnetic field applied normal to the plane. The solid line is a linear fit to the zero-field data below $130\mathrm{mK}$. The dashed line shows the behavior of a Fermi liquid consisting of the expected electronic part extracted from the Wiedemann-Franz law using the residual resistivity ${\rho }_0$ for this sample obtained at high magnetic and a phonon contribution given by the solid line (zero-field data). From 167. The [near (0,1)] and [near (0,0.5)] dots are estimates for the coefficient of the electronic contribution for monotonic and nonmonotonic gap functions as given in the text. The experimental data show a zero $y$ intercept because of electron-phonon decoupling at low temperature. (Bottom) Thermal conductivity of an optimal PCCO single crystal for a heat current in the basal plane, plotted as $\kappa ∕T$ vs $T^{1.7}$. These data show the downturn to the decoupling of the electron and phonons. Note that the data above the downturn go as a power of 1.7 and not 2. Courtesy of Taillefer.

Figure 45

(Color online) ${}^{63}\mathrm{Cu}$ spin-relaxation rate $1∕T_1$ as a function of temperature in the superconducting and normal states of a ${\mathrm{Pr}}_{0.91}\mathrm{La}{\mathrm{Ce}}_{0.09}\mathrm{Cu}{\mathrm{O}}_{4-y}$ single crystal. Solid circles: data in the superconducting state measured with a magnetic field of $6.2\mathrm{T}$ parallel to the $\mathrm{Cu}{\mathrm{O}}_2$ planes. Open black circles: data in the normal state measured with an out-of-plane magnetic field of $15.3\mathrm{T}$. The solid line is a fit using a $d_{x^2-y^2}$ order parameter leading with $2{\Delta }_0=3.8k_B{T}_c$. The solid line is a fit to the Korringa law, which is consistent with Fermi-liquid behavior. From 547.

Figure 46

(Color online) Tricrystal geometry to measure symmetry of order parameter. (a) Tricrystal geometry used to force phase frustration and spontaneous generation of a half-flux quantum at the tricrystal junction point. The arrows indicate the diagonal and horizontal grain boundaries. (b) 3D image of the flux threading the film. Adapted from 483.

Figure 47

Zigzag ramp-edge Josephson junctions made of ${\mathrm{Nd}}_{2-x}{\mathrm{Ce}}_x\mathrm{Cu}{\mathrm{O}}_4$ and conventional $s$-wave Nb. (a) Top view of the zigzag design. (b) Cross-section view of a ramp-edge junction including a thin interlayer of NCCO. Examples of anomalous field modulations of the critical current arising from the $d$-wave symmetry for devices made of (c) eight facets of $25\mu \mathrm{m}$ width and (d) 80 facets of $5\mu \mathrm{m}$ width. From 26.

Figure 48

(Color online) Photoemission valence-band spectra of ${\mathrm{Nd}}_{1.85}{\mathrm{Ce}}_{0.15}\mathrm{Cu}{\mathrm{O}}_{4-\delta }$, ${\mathrm{Nd}}_2\mathrm{Cu}{\mathrm{O}}_4$, ${\mathrm{La}}_2\mathrm{Cu}{\mathrm{O}}_4$, and ${\mathrm{La}}_{1.85}{\mathrm{Sr}}_{0.15}\mathrm{Cu}{\mathrm{O}}_4$ taken $5\mathrm{eV}$ below the $\mathrm{Cu}{L}_3$ edge. Energies of the spectra are aligned with respect to the $\mathrm{Cu}3d^8$ ${}^{1}G$ final states. From 445.

Figure 49

(Color online) Schematic of the energy levels of LSCO and NCCO obtained from Anderson impurity model calculations and x-ray photoemission. OPG is the optical gap from undoped materials. Shaded regions represent occupied density of states. The manifold of $\mathrm{O}2p$ bands are found to be displaced relative to the primarily Cu derived Hubbard-like bands between LSCO and NCCO. This explains the small shift in the $\mathrm{O}1s$ core-level data when comparing hole- and electron-doped data. From 454.

Figure 50

Peak height of the ${\mathrm{Cu}}^{+}4p_{\pi }$ spectral feature in the $\mathrm{Cu}K$-edge XAS spectra as a function of Ce concentration for various $\left(R\right)\mathrm{CCO}$ compounds. Its intensity is approximately proportional to the $3d^{10}$ occupation. From 273.

Figure 51

(Color online) Comparison of the phonon anomaly in the bond-stretching branches observed via neutron scattering in a number of metallic oxide perovskites. (Left) [100] direction. (Right) [110] direction. From 60.

Figure 52

The significance of chemical potential shift. (Top) Chemical potential shift $\mu$ in NCCO and LSCO. (Middle) Incommensurability measured by inelastic neutron-scattering experiments as given by 527, 525. In the hatched region, the incommensurability varies linearly and $\Delta \mu$ is constant as functions of doping level. (Bottom) $\mu \text{−}T$ phase diagram of NCCO and LSCO. Note that there is an uncertainty in the absolute value of the chemical potential jump between NCO and LCO. From 160.

Figure 53

Comparison of charge conductivity $\sigma \left(T\right)=1∕\rho \left(T\right)$, plotted as $L_0∕\rho \left(T\right)$ (triangles) (i.e., given by the Wiedemann-Franz expectation), and electronic contribution to the heat conductivity ${\kappa }_e$, plotted as ${\kappa }_e∕T$ (circles), as a function of temperature in the normal state at $H=13\mathrm{T}$. A clear violation of the Wiedemann-Franz law is found (167). The downturn below $300\mathrm{mK}$ is an artifact of thermal decoupling of the electronic and phononic degrees of freedom (436), but an approximately factor of 2 discrepancy remains in the magnitude of the thermal conductivity and the value inferred from the charge conductivity at low temperature.

Figure 54

(Color online) ARPES on SCCO. (a) Measured ARPES spectral function along the AFBZ as given by the arrow in (b). The SDW gap $2V_{\pi ,\pi }$ is readily visible in the raw spectra. (b) Schematic of the band structure from a $\sqrt{2}\times \sqrt{2}$ reconstruction. Adapted from 359.

Figure 55

Calculation of the optical conductivity based on the SDW band structure in Fig. 54. Spectra were calculated for a $x=0.13$ doping with a value of $2V_{\pi \pi }=0.25\mathrm{eV}$ and a gap opening temperature of $170\mathrm{K}$. The symbols are the measured optical conductivity for $x=0.13$ and the lines the spin-density-wave model calculation. Compare also to the $x=0.10$ data in Fig. 32. From 550.

Figure 56

(Color online) Schematic of the phase diagram of ${\mathrm{Pr}}_{2-x}{\mathrm{Ce}}_x\mathrm{Cu}{\mathrm{O}}_4$ from resistivity measurements in magnetic field high enough to suppress superconductivity. Plotted as dots is $T_0$, the temperature below which the $T^2$ behavior is observed. At dopings lower than that of the nominal QCP the resistivity shows a low-temperature upturn (98).

Figure 57

(Color online) Proposed phase diagram for field stabilized magnetism for the cuprates. The phase diagram includes a transition from a large FS to a small FS at fields above $H_{c2}$. The transition happens at a doping $x_m$ which is greater than the doping where the SDW is suppressed at zero field. From 399.

Figure 58

The $x$ variation of the pseudogap. (Top) Magnitude of ${\Delta }_{\mathrm{PG}}$ as defined by the higher-lying isosbetic (equal-absorption) point in the temperature-dependent conductivity spectra and the magnitude of the pseudogap $\left({\omega }_{\mathrm{PES}}\right)$ in the photoemission spectra (32) (Ref. 26 in the figure). The ${\omega }_{\mathrm{PES}}$ is defined as the maximum energy of the quasiparticle peak on the putative large Fermi surface in the ARPES spectra shown in Figs. 2(c)–2(e) of 32. (Bottom) The obtained phase diagram. The onset temperature of pseudogap formation $T^{*}$ and the crossover temperature of out-of-plane resistivity $T_{\rho }$ [as given by the arrows in Fig. 19 (right)] are plotted against $x$ together with the Néel temperature $T_N$ reported previously by 280 (Ref. 19 in the figure).