arXiv subjects

W. N. Hardy

Publications and source records attributed to W. N. Hardy.

At least 163 records · Page 9Linked to original sources

arXiv2005

The a-axis optical conductivity of detwinned ortho-II YBa_2Cu_3O_6.50

The a-axis optical properties of a detwinned single crystal of YBa_2Cu_3O_6.50 in the ortho II phase (Ortho II Y123, T_c= 59 K) were determined from reflectance data over a wide frequency range (70 - 42 000 cm^-1) for nine temperature values between 28 and 295 K. Above 200 K the spectra are dominated by a broad background of scattering that extends to 1 eV. Below 200 K a shoulder in the reflectance appears and signals the onset of scattering at 400 cm^-1. In this temperature range we also observe a peak in the optical conductivity at 177 cm^-1. Below 59 K, the superconducting transition temperature, the spectra change dramatically with the appearance of the superconducting condensate. Its spectral weight is consistent, to within experimental error, with the Ferrell-Glover-Tinkham (FGT) sum rule. We also compare our data with magnetic neutron scattering on samples from the same source that show a strong resonance at 31 meV. We find that the scattering rates can be modeled as the combined effect of the neutron resonance and a bosonic background in the presence of a density of states with a pseudogap. The model shows that the decreasing amplitude of the neutron resonance with temperature is compensated for by an increasing of the bosonic background yielding a net temperature independent scattering rate at high frequencies. This is in agreement with the experiments.

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arXiv2005

Delocalized fermions in underdoped cuprates

Low temperature heat transport was used to investigate the ground state of high-purity single crystals of the lightly-doped cuprate YBa$_{2}$Cu$_{3}$O$_{6.33}$. Samples were measured on either side of the superconducting phase boundary, in both zero and applied magnetic field. We report the observation of delocalized fermionic excitations at zero energy in the non-superconducting state, which shows that the ground state of underdoped cuprates is metallic. Its low-energy spectrum appears to be similar to that of the d-wave superconductor, i.e. nodal. The insulating ground state observed in underdoped La$_{2-x}$Sr$_{x}$CuO$_4$ is attributed to the competing spin-density-wave order present in that system.

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arXiv2005

Coherence, incoherence and scaling along the c axis of YBa_2Cu_3O_{6+x}

The optical properties of single crystals of YBa_2Cu_3O_{6+x} have been examined along the c axis above and below the critical temperature (T_c) for a wide range of oxygen dopings. The temperature dependence of the optically-determined value of the dc conductivity (σ_{dc}) in the normal state suggests a crossover from incoherent (hopping-type) transport at lower oxygen dopings (x \lesssim 0.9) to more coherent anisotropic three-dimensional behavior in the overdoped (x \approx 0.99) material at temperatures close to T_c. The assumption that superconductivity occurs along the c axis through the Josephson effect yields a scaling relation between the strength of the superconducting condensate (ρ_{s,c}, a measure of the number of superconducting carriers), the critical temperature, and the normal-state c-axis value for σ_{dc} just above T_c; ρ_{s,c} \propto σ_{dc} T_c. This scaling relation is observed along the c axis for all oxygen dopings, as well as several other cuprate materials. However, the agreement with the Josephson coupling model does not necessarily imply incoherent transport, suggesting that these materials may indeed be tending towards coherent behavior at the higher oxygen dopings.

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arXiv2004

From incommensurate to dispersive spin-fluctuations: The high-energy inelastic spectrum in superconducting YBa2Cu3O6.5

We have investigated the spin fluctuations at energy transfers up to ~110 meV, well above the resonance energy (33 meV) in the YBa2Cu3O6.5 ortho-II superconductor using neutron time-of-flight and triple-axis techniques. The spectrum at high energies differs from the low-energy incommensurate modulations previously reported where the incommensurate wave vector is largely independent of energy. Well above the resonance the peak of the spin response lies at wave vectors that increase with energy. Within error the excitations at all energies above the resonance are best described by a ring around the (pi, pi) position. The isotropic wave-vector pattern differs from a recently reported square pattern in different but related systems. The spin spectral weight at high-energies is similar to that in the insulator but the characteristic velocity is ~40% lower. We introduce a method of extracting the acoustic and optic weights at all energies from time-of-flight data. We find that the optic spectral weight extends to surprisingly low-energies of ~25 meV, and infer that the bilayer spin correlations weaken with increase in hole doping. When the low-energy optic excitations are taken into account we measure the total integrated weight around (pi, pi), for energies below 120 meV, to agree with that expected from the insulator. As a qualitative guide, we compare spin-wave calculations for an ordered and a disordered stripe model and describe the inadequacy of this and other stripe models for the high-energy fluctuations.

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arXiv2004

Universal scaling relation in high-temperature superconductors

Scaling laws express a systematic and universal simplicity among complex systems in nature. For example, such laws are of enormous significance in biology. Scaling relations are also important in the physical sciences. The seminal 1986 discovery of high transition-temperature (high-T_c) superconductivity in cuprate materials has sparked an intensive investigation of these and related complex oxides, yet the mechanism for superconductivity is still not agreed upon. In addition, no universal scaling law involving such fundamental properties as T_c and the superfluid density ρ_s, a quantity indicative of the number of charge carriers in the superconducting state, has been discovered. Here we demonstrate that the scaling relation ρ_s \propto σ_{dc} T_c, where the conductivity σ_{dc} characterizes the unidirectional, constant flow of electric charge carriers just above T_c, universally holds for a wide variety of materials and doping levels. This surprising unifying observation is likely to have important consequences for theories of high-T_c superconductivity.

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arXiv2004

Absolute values of the London penetration depth in YBa2Cu3O6+y measured by zero field ESR spectroscopy on Gd doped single crystals

Zero-field electron spin resonance (ESR) of dilute Gd ions substituted for Y in the cuprate superconductor YBa$_2$Cu$_3$O$_{\rm 6+y}$ is used as a novel technique for measuring the absolute value of the low temperature magnetic penetration depth $λ(T\to 0)$. The Gd ESR spectrum of samples with $\approx 1%$ substitution was obtained with a broadband microwave technique that measures power absorption bolometrically from 0.5 GHz to 21 GHz. This ESR spectrum is determined by the crystal field that lifts the level degeneracy of the spin 7/2 Gd$^{3+}$ ion and details of this spectrum provide information concerning oxygen ordering in the samples. The magnetic penetration depth is obtained by relating the number of Gd ions exposed to the microwave magnetic field to the frequency-integrated intensity of the observed ESR transitions. This technique has allowed us to determine precise values of $λ$ for screening currents flowing in the three crystallographic orientations ($\hat a$, $\hat b$ and $\hat c$) in samples of Gd$_{\rm x}$Y$_{\rm 1-x}$Ba$_2$Cu$_3$O$_{6+{\rm y}}$ of three different oxygen contents ${\rm y}=0.993$ ($T_c = 89$ K), ${\rm y}=0.77$ ($T_c=75$ K) and ${\rm y}=0.52$ ($T_c=56$ K). The in-plane values are found to depart substantially from the widely reported relation $T_c\propto 1/λ^2$.

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arXiv2004

Zooming-in on the charge ordering in YBa2Cu3O6.5

We report direct evidence of charge/orbital ordering of low energy electronic states of $Cu$ in YBa$_2$Cu$_3$O$_{6+x}$ ortho-II phase in both the $CuO_3$ chain and the CuO$_2$ plane. Huge enhancement of the $({1/2},0,0)$ superstructure Bragg peak is observed when photon energy is tuned to the $Cu L_{2,3}$ absorption edge with large polarization dependence. The ordering in the $CuO_2$ plane discovered here sheds new light on how the one dimensional $Cu-O$ chains affect the $CuO_2$ plane, and why many normal and superconducting state properties of this system exhibit strong anisotropy.

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arXiv2003

Dynamic Stripes and Resonance in the Superconducting and Normal Phases of YBa2Cu3O6.5 Ortho-II Superconductor

We describe the relation between spin fluctuations and superconductivity in a highly-ordered sample of YBaCu3O6.5 using both polarized and unpolarized neutron inelastic scattering. The spin susceptibility in the superconducting phase exhibits one-dimensional incommensurate modulations at low-energies, consistent with hydrodynamic stripes. With increasing energy the susceptibility curves upward to a commensurate, intense, well-defined and asymmetric resonance at 33 meV with a precipitous high-energy cutoff. In the normal phase, which we show is gapless, the resonance remains surprisingly strong and persists clearly in Q scans and energy scans. Its similar asymmetric spectral form above Tc=59 K suggests that incoherent superconducting pairing fluctuations are present in the normal state. On cooling, the resonance and the stripe modulations grow in well above Tc below a temperature that is comparable to the pseudogap temperature where suppression occurs in local and low-momentum properties. The spectral weight that accrues to the resonance is largely acquired by transfer from suppressed low-energy fluctuations. We find the resonance to be isotropically polarized, consistent with a triplet carrying ~2.6% of the total spectral weight of the Cu spins in the planes.

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arXiv2003

Survival of the d-wave superconducting state near the edge of antiferromagnetism in the cuprate phase diagram

In the cuprate superconductor $YBa_2Cu_3O_{6+x}$, hole doping in the $CuO_2$ layers is controlled by both oxygen content and the degree of oxygen-ordering. At the composition $\rm YBa_2Cu_3O_{6.35}$, the ordering can occur at room temperature, thereby tuning the hole doping so that the superconducting critical temperature gradually rises from zero to 20 K. Here we exploit this to study the c-axis penetration depth as a function of temperature and doping. The temperature dependence shows the d-wave superconductor surviving to very low doping, with no sign of another ordered phase interfering with the nodal quasiparticles. The only apparent doping dependence is a smooth decline of superfluid density as Tc decreases.

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arXiv2003

Microwave Spectroscopy of PrOs_4Sb_12: Josephson-Coupled Two-Band Superconductivity and Itinerant f Electrons

We report microwave surface impedance measurements made on a single crystal of PrOs_4Sb_12 across the frequency range 0.5 to 21 GHz. The penetration depth data provide clear thermodynamic evidence for superconductivity arising in two bands coupled by Josephson pair-tunneling, indicating two order parameters with the same symmetry. Detailed conductivity spectra obtained using high-resolution bolometry confirm this picture and extend it, revealing the itinerant nature of the Pr f electrons through the observation of quasiparticles with heavily renormalized mass.

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arXiv2003

Cu NMR Study of Detwinned Single Crystals of Ortho--II YBCO6.5

Copper NMR has been used as a local probe of the oxygen ordering in Ortho--II YBa2Cu3O6.5 crystals grown in BaZrO3 crucibles. Line assignments have been made to each of the expected crystallographically inequivalent sites. The presence of distinct and narrow lines for these sites as well as the lack of a line known to be associated with oxygen defects indicates that these crystals are highly stoichiometric. Our estimate of the lower limit on the chain length is consistent with that derived from X-ray diffraction measurements. In addition, we have found no evidence for static magnetic moments, in contrast to some previous results.

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arXiv2003

Diffusion of Nonequilibrium Quasiparticles in a Cuprate Superconductor

We report a transport study of nonequilibrium quasiparticles in a high-Tc cuprate superconductor using the transient grating technique. Low-intensity laser excitation (at photon energy 1.5 eV) was used to introduce a spatially periodic density of quasiparticles into a high-quality untwinned single crystal of YBa2Cu3O6.5. Probing the evolution of the initial density through space and time yielded the quasiparticle diffusion coefficient, and both inelastic and elastic scattering rates. The technique reported here is potentially applicable to precision measurement of quasiparticle dynamics, not only in cuprate superconductors, but in other electronic systems as well.

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arXiv2003

Single-quasiparticle stability and quasiparticle-pair decay in YBa2Cu3O6.5 (Ortho II)

We report results and analysis of time-resolved photoinduced reflectivity experiments on the cuprate superconductor YBa2Cu3O6.5. The sample, which has Tc=45 K, was characterized by a high degree of purity and Ortho II ordering. The change in reflectivity (Delta R) was induced and probed using pulses of 100 femtosecond duration and photon energy 1.55 eV from a Ti:Sapphire laser. We provide a detailed picture of the decay rate (gamma) of Delta R as a function of temperature T and pump intensity I. At low T, gamma decreases linearly with decreasing I, extrapolating to nearly zero in the limit that I tends to zero. At higher temperatures gamma has the same linear dependence, but with nonzero limit as I goes to zero. In the interpretation of these results we assume that Delta R is proportional to the nonequilibrium quasiparticle density created by the laser. From an analysis of the gamma vs. I we estimate beta, the coefficient of proportionality relating the quasiparticle decay rate to the density. The intercept of gamma vs. I yields the thermal equilibrium quasiparticle decay rate. In a discussion section, we argue that the quasiparticles induced by the laser occupy primarily states near the antinodal regions of the Brillouin zone. We explain the divergence of the lifetime as T and I both tend to zero as a consequence of momentum and energy conservation in electron-electron scattering. We discuss the significance of the measured value of beta (approximately 0.1 cm2/s) in terms of the electron-phonon interactions.

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arXiv2003

Sum rules and energy scales in the high-temperature superconductor YBa2Cu3O6+x

The Ferrell-Glover-Tinkham (FGT) sum rule has been applied to the temperature dependence of the in-plane optical conductivity of optimally-doped YBa_2Cu_3O_{6.95} and underdoped YBa_2Cu_3O_{6.60}. Within the accuracy of the experiment, the sum rule is obeyed in both materials. However, the energy scale ω_c required to recover the full strength of the superfluid ρ_s in the two materials is dramatically different; ω_c \simeq 800 cm^{-1} in the optimally doped system (close to twice the maximum of the superconducting gap, 2Δ_0), but ω_c \gtrsim 5000 cm^{-1} in the underdoped system. In both materials, the normal-state scattering rate close to the critical temperature is small, Γ< 2Δ_0, so that the materials are not in the dirty limit and the relevant energy scale for ρ_s in a BCS material should be twice the energy gap. The FGT sum rule in the optimally-doped material suggests that the majority of the spectral weight of the condensate comes from energies below 2Δ_0, which is consistent with a BCS material in which the condensate originates from a Fermi liquid normal state. In the underdoped material the larger energy scale may be a result of the non-Fermi liquid nature of the normal state. The dramatically different energy scales suggest that the nature of the normal state creates specific conditions for observing the different aspects of what is presumably a central mechanism for superconductivity in these materials.

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arXiv2003

Bolometric technique for high-resolution broadband microwave spectroscopy of ultra-low-loss samples

A novel low temperature bolometric method has been devised and implemented for high-precision measurements of the microwave surface resistance of small single-crystal platelet samples having very low absorption, as a continuous function of frequency. The key to the success of this non-resonant method is the in-situ use of a normal metal reference sample that calibrates the absolute rf field strength. The sample temperature can be controlled independently of the 1.2 K liquid helium bath, allowing for measurements of the temperature evolution of the absorption. However, the instrument's sensitivity decreases at higher temperatures, placing a limit on the useful temperature range. Using this method, the minimum detectable power at 1.3 K is 1.5 pW, corresponding to a surface resistance sensitivity of $\approx$1 $μΩ$ for a typical 1 mm$\times$1 mm platelet sample.

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arXiv2003

Transport in Ultraclean YBa$_2$Cu$_3$O$_7$: neither Unitary nor Born Impurity Scattering

The thermal conductivity of ultraclean YBa$_2$Cu$_3$O$_7$ was measured at very low temperature in magnetic fields up to 13 T. The temperature and field dependence of the electronic heat conductivity show that two widespread assumptions of transport theory applied to unconventional superconductors fail for clean cuprates: impurity scattering cannot be treated in the usual unitary limit (nor indeed in the Born limit), and scattering of quasiparticles off vortices cannot be neglected. Our study also sheds light on the long-standing puzzle of a sudden onset of a "plateau" in the thermal conductivity of Bi-2212 versus field.

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arXiv2003

Doping dependence of superconducting gap in YBa_2Cu_3O_y from universal heat transport

Thermal transport in the T -> 0 limit was measured as a function of doping in high-quality single crystals of the cuprate superconductor YBa_2Cu_3O_y. The residual linear term kappa_0/T is found to decrease as one moves from the overdoped regime towards the Mott insulator region of the phase diagram. The doping dependence of the low-energy quasiparticle gap extracted from kappa_0/T is seen to scale closely with that of the pseudogap, arguing against a non-superconducting origin for the pseudogap. The presence of a linear term for all dopings is evidence against the existence of a quantum phase transition to an order parameter with a complex (ix) component.

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arXiv2003

Thermal Conductivity across the Phase Diagram of Cuprates: Low-Energy Quasiparticles and Doping Dependence of the Superconducting Gap

Heat transport in the cuprate superconductors YBa$_2$Cu$_3$O$_{y}$ and La$_{2-x}$Sr$_x$CuO$_4$ was measured at low temperatures as a function of doping. A residual linear term kappa_{0}/T is observed throughout the superconducting region and it decreases steadily as the Mott insulator is approached from the overdoped regime. The low-energy quasiparticle gap extracted from kappa_{0}/T is seen to scale closely with the pseudogap. The ubiquitous presence of nodes and the tracking of the pseudogap shows that the overall gap remains of the pure d-wave form throughout the phase diagram, which excludes the possibility of a complex component (ix) appearing at a putative quantum phase transition and argues against a non-superconducting origin to the pseudogap. A comparison with superfluid density measurements reveals that the quasiparticle effective charge is weakly dependent on doping and close to unity.

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