Quantized Vortices and Diamagnetic Precursor to the Meissner State in High-T c Superconductors

We report the magnetic imaging for underdoped and optimally-dopedLa_2–x Sr _x CuO₄ (LSCO) thin films on single substrates and nearly optimallydoped YBa₂Cu₃O_7–x (YBCO) thin films on tricrystal substrates in the temperature range both below and above T _c using scanning SQUID microscopy. Below T _c, clear integer- and half-integer quantized vortices were observable. Above T _c, however, the inhomogeneous diamagnetic domains appeared. The local diamagnetic domains that led to the Meissner state were found in the broad temperature range for underdoped samples and in the narrow limited temperature range for optimally-doped samples. The results provide evidence that local diamagnetic domains are closely related to the pseudogap state. The continuous connection of the domain state above T _c with the state of a half-integer vortex at the tricritical point in the YBCO film below T _c also indicates that the diamagnetic domains are also closely related to the occurrence of d_x ^{2-y 2}-wave superconductivity.     

Microwave Measurements of Overdoped Y0.9Ca0.1Ba2Cu3O7−δ Thin Films

In the present report we show, for the first time, that a complex order parameter is not just a surface effect, but a bulk property in overdoped Y_0.9Ca_0.1Ba₂Cu₃O_7– thin films. The penetration depth change versus temperature is very well fitted to a complex order parameter of the form d_x ^{2-y 2} + id _xy , where = 14.5 meV and = 2meV. This result contrasts our previous results for optimally doped YBCO thin films where a power law for the penetration depth, versus temperature was reported, corresponding to a d_x ^{2-y 2}-wave order parameter. The penetration depth behavior is accompanied by a rapid reduction of the scattering rate at low temperatures, in contrast with a flattening of this quantity for the optimally doped YBCO films.     

In-Plane Anisotropy of the Upper Critical Field of La2−x Sr x CuO4 in the Underdoped and Overdoped Regimes

For La_2–x Sr _x CuO₄ single-crystals in the underdoped and overdoped regimes, we have measured the electrical resistivity along the c-axis, _c , under constant magnetic fields, changing the field direction in the ab-plane. At x=0.08, 0.12 and 0.16 in the underdoped and almost optimally-doped regimes, clear anisotropy of _c with the fourfold symmetry in the ab-plane has been observed. This symmetry is regarded as the fourfold symmetry of the upper critical field, H _c2, and explained as being mainly due to the anisotropy of the superconducting energy gap owing to the d_x ^{2-y 2} pairing. The magnitude of the fourfold component of H _c2, H _c2/H _c2, is largest in x=0.08 among the three crystals. At x=0.20 in the overdoped regime, no clear fourfold symmetry has been observed. It appears that the fourfold symmetry is easy to observe in the underdoped regime rather than in the overdoped regime.     

Doping-Dependent Superconducting Symmetry in Hubbard Systems

The d-wave superconducting state is studied by using a generalized Hubbard model, in which a next-nearest-neighbor correlated-hopping interaction (t ₃) is included. The results obtained within the BCS framework suggest the existence of a critical hole concentration, below which a d_x ^{2-y 2}-wave superconducting gap is observed. However, above this critical concentration the maxima of the single-particle excitation energy gap are rotated by /4 and no real nodes exist, as observed in tunneling experiments. In this study, the parameters estimated by first-principle calculations for cuprate superconductors are used.     

Correlation Between the Superfluid Density ns(T) ∝ 1/λ2ab(T) at Low Temperatures and Nanostructures in the a–b Planes of YBCO

A correlation between the superfluid density n _s(T) 1/² _ab(T) at low temperatures and the nanoscopic disorder in the a–b planes of YBCO thin films has been revealed. It has been found that a degree of this disorder can be determined from the two-component dependence of the critical current density on temperature. These findings are consistent with a discovery of a nanodomain structure in the a–b planes of an optimally doped YBCO [J. Etheridge, Phil. Mag. A73, 643 (1996)].     

Use of tricrystal junctions to probe the pairing state symmetry of YBa2Cu3O7

We have developed a new method of probing superconducting pairing state symmetry, by using tricrystal devices analogous tos-d corner junctions. Two central peaks are observed in the field-modulated critical currents of frustrated YBCO tricrystal junctions operating in the short junction limit, consistent with predominantly — wave pairing symmetry with little or no imaginarys-wave component. However, our results are consistent with a real combination of larged-wave and smalls-wave components. A single peak is also observed for frustrated tricrystal junctions operating in the long junction limit, and it is shown theoretically that the behaviors ofs- andd-wave superconductors are indistinguishable in this limit.     

Spin Injection in High-T c Cuprates: An STM Spectroscopy Study

To study how the high-T _c order parameter (OP) evolves under the injection of spin-polarized quasiparticles, STM spectroscopy has been performed on superconductor/ferromagnet thin-film heterostructures comprising YBa₂Cu₃O_7–x (YBCO) and La_0.7Ca_0.3MnO₃ (LCMO) at 4.2 K. Quasiparticle-tunneling and Andreev-reflection characteristics measured on the YBCO under spin-injection from the LCMO were analyzed with the d-wave Blonder-Tinkham-Klapwijk theory, to reveal a spectral evolution which provides direct evidence for dynamic magnetic pair-breaking. The spectral analysis also shows the d-wave OP to remain time-reversal invariant as it is suppressed by the spin-injection. These results are discussed in terms of the general search for quantum-critical points in the high-T _c phase diagram.     

Symmetries of Vortex Lattice Solutions of the Bogoliubov–de Gennes Equation in a Two-Dimensional Square Lattice

This report describes symmetry properties of tetragonal vortex lattice solutions of the Bogoliubov–de Gennes equation in a two-dimensional square lattice in a uniform magnetic field. The invariance group of a tetragonal vortex lattice solution is expressed in a form of G _(l) = (e + tC _2x ) (l = 0, 2, ± 1), where tC _2x is a space rotation around the x-axis accompanied with time reversal, is a kind of fourfold rotation group, and L is the magnetic translational group of the vortex lattice state. We give a new, refined definition of local symmetric order parameters (OPs) (s-wave, d-wave, and p-wave), which have a well-defined nature such that the OP (e.g., s-wave OP) at the translated site by a lattice vector (of the vortex lattice) from a site (m, n) is expressed by the OP (e.g., s-wave) at the site (m, n) times a phase factor. Winding numbers around the origin of s-wave and d-wave OPs are obtained for four types of solutions G _(l) (l = 0, 2, ± 1). It is shown that all energy bands of quasiparticles of a vortex lattice state are doubly degenerate.     

Direct Comparison of Andreev Bound States Formed at Different Interfaces Using YBa2Cu3O7−y /I/Ag Ramp-edge Junctions

We present the measurements on quasiparticle tunneling using YBa ₂ Cu ₃ O _7–y /I/Ag ramp-edge junctions to clarify the zero bias conductance peak(ZBCP) related to the Andreev bound states . Two junctions with different tilt angles(0° and 45°) between the a-axis of YBCO and the junction boundary are fabricated on the same substrate simultaneously using pulsed laser deposition and Ar ion milling techniques. For the junctions with the tilted angle of 45° ((110) tunneling), a pronounced ZBCP was always observable, whereas for those fabricated with the tilted angle of 0°, a dip structure at zero bias or a very weak ZBCP was mostly observed. The results are consistent with the recent studies on the Andreev reflection between a -wave superconductor and a normal metal.     

High-Quality YBa2Cu3O7?x Films with CeO2/YSZ Buffer Layers on 2-Inch Si Wafers Deposited by Pulsed Laser

The pulsed laser deposition (PLD) process is shown for in situ reproducibly fabricating YBa₂Cu₃O_7–x (YBCO) superconducting films with yttrium-stabilized zirconia (YSZ) and CeO₂ buffer layers, nonsuperconducting crystalline YBa₂Cu₃O_7–x (YBCO*) passivation layer, and silver contact film on 2-inch silicon wafers. Variations of less than ±7% in film thickness have been obtained for this multilayer growth over the whole wafer. The YBCO films on 2-inch silicon wafers have homogeneous superconducting properties with zero resistance temperature T _c0 from 88.4 K to 88.9 K. and critical current density J _c at 77 K and zero field from 2.5 × 10⁶ to 7× 10⁶ A/cm². The YSZ, CeO₂ and YBCO layers grow epitaxially on silicon wafers. Full widths at half maximum (FWHMs) of (113) reflections of 40 nm thick YBCO layer from -scan patterns are only 1.71° and 1.85° corresponding to the center and edge of the wafer, respectively. These results are very promising for developing high-quality high-T _c superconducting devices on large-area silicon wafers.     

Out-of-plane quasiparticle dynamics of the cuprate superconductors belowT c in microwave region

We have investigated the anisotropic quasiparticle conductivity in the superconducting state for microwave frequencies in YBa₂Cu₃O_7– (YBCO) and La_2–xSr_xCuO₄ (LSCO) with several hole concentrations. Common features were found for YBCO and LSCO. That is, in underdoped materials, the strong two dimensional nature was found to be retained even below T_c. On the other hand, in optimally doped and overdoped materials, the anisotropy decreases rapidly below T_c. In particular, in YBCO, it is suggested that the c-axis transport becomes coherent below T_c.     

Investigation of the Symmetry of the Pairing State in YBa2Cu3O7?δ Using the Nonlinear Transverse Magnetic Moment: Experimental Results

Measurements of the nonlinear transverse magnetic moment have been carried out on disk-shaped samples of YBCO, using an ac technique. Numerical calculations for a d _x ² - _y ² pairing state predict a fourfold modulation of this moment as a function of the angle between the applied magnetic and the crystalline axes for a magnetic field applied in the a–b plane of the sample. Our results imply a minimum nonzero gap at all points on the Fermi surface.     

A Hidden Order in the Cuprate Superconductors: The d-Density-Wave Phase

We study the electronic structure near impurities in the d-density-wave (DDW) state, a possible candidate phase for the pseudo-gap region of the high-temperature superconductors. We show that the density of states near a nonmagnetic impurity in the DDW state is qualitatively different from that in a superconductor with d_x ²-y² symmetry. Thus the electronic structure near impuritiescan provide insight into the nature of the two phases recently observed by scanning tunneling microscopy experiments in the superconducting state of underdoped Bi-2212 compounds.     

Study of the Order Parameter Symmetry in Overdoped Y1−x Ca x Ba2Cu3O7−δ by Measurement of Andreev Reflection, Evidence for Enhancement of the Sub Dominant Order Parameter Amplitude in High Transparency Contacts

We have measured the differential conductance of Au/Y_1–x Ca _x Ba₂Cu₃O_7– point contacts in the regime where it is dominated by Andreev reflection, which enhances its value at low bias. We find that the characteristics can not be fitted by a pure d-wave Order Parameter (OP). Using the formalism developed by Kashiwaya and Tanaka, the best fits are obtained by adding a sub-dominant imaginary OP, whose amplitude appears to depend on the transparency of the contact. At high transparencies it can reach up to 60% of the total amplitude of the OP, for lower transparencies it is substantially smaller. We attribute this enhancement, at high transparencies to a proximity effect between the Au tip and the superconducting electrode.     

Raman Spectroscopy, Structural Modifications, and Phase Transitions in the High-Temperature Superconductors

The formation of phases is investigated from a systematic study of the Raman active phonons in the whole range of oxygen doping of YBa₂Cu₃O _x (6 < x < 7). Changes in the spectral characteristics of the in-phase vibrations of the plane oxygen atoms in the overdoped region are related, with slight modifications of the buckling in the CuO₂ planes. A softening of the A _g symmetry apical oxygen phonon is accompanied with an increase in the intensity of the high-frequency mode at 600 cm^–1 and attributed to the breaking of the chains into small segments. The analysis of the apex and the in-phase phonon modes indicates the formation of superstructures, which are embedded as spatially separated phases in the whole oxygen concentration region of 6.35 < x < 6.95. A similar separation into small domains of phases may also occur in the underdoped compounds (x < 6.35) down to a critical oxygen concentration at x 6.15, where the system breaks into randomly oriented small chains.     

Role of Stripes in Spin and Charge Dynamics of Underdoped La2−x Sr x CuO4

We investigate the electronic states of underdoped La _2–x Sr _x CuO ₄ (LSCO) by using a microscopic model, i.e., t-t-t-J model, containing charge stripes. The numerically exact diagonalization calculation is employed on small clusters. The physical properties observed in the angle-resolved photoemission and optical conductivity experiments are consistently explained in the model with vertical stripes, but not diagonal ones. These results demonstrate a crucial role of the vertical stripes in underdoped LSCO.     

Effect of Normal-State Pseudogap on Physical Quantities in Hubbard Model for Underdoped High-T c Cuprates

We develop the strong-coupling theory of coexisting charge-density-wave (CDW) and superconductivityd-wave gaps within the framework of the FLEX (fluctuation exchange) approximation for the two-dimensional Hubbard model. For nested sections of the Fermi surface these equations reduce to the previous FLEX equations for superconductivity where the squared energy gap _s ² in the denominator of the Green's function is replaced by ( _s ² + _c ² ) (here _s is the superconductivity and _c the CDW gap). We solve these equations by taking for _c a phenomenologicald-wave gap. The resulting neutron scattering intensity, spin-lattice relaxation rate 1/T₁ , Knight shift, resistivity, and photoemission intensity are in qualitative agreement with the data on underdoped high-T_c cuprates. TheT_c for superconductivity decreases and the crossover temperature T_* for 1/T₁Tincreases with increasing gap amplitude of _c which is in qualitative agreement with the phase diagram for underdoped cuprates.     

Comparative study of shunted bicrystal Josephson junctions

In order to optimize the series array performance of Y Ba₂Cu₃O_7−x (YBCO) grain boundary shunted junctions, a method to determine and control the junction resistance R_s and Au/YBCO contact resistivity ρ _c has been developed. 200 nm thick c-oriented YBCO films were grown by intermittent thermal coevaporation on bicrystal yttria-stabilized zirconia substrates. A gold contact overlayer of thickness d_n was deposited in situ. Normal junction resistances have been measured as a function of d_n and shunt width w. It was shown that, in accordance with theoretical estimates, the junction shunt resistance is essentially controlled by the c-axis Au/YBCO interface specific resistance and scales as . The product ρ _c ρ _n ≃ 3.10⁻¹⁴ Ω² cm ³ was estimated from the experimental data, leading to ρ _c ≈ 10⁻⁸ Ωcm ² for typical values of ρ _n for gold thin films.     

Disk Resonators as Nonlinear Surface Impedance Measurement Tools

The edge-current–free rotational symmetric disk resonator mode, TM₀₁₀, was used as characterization tool for nonlinear surface impedance measurement of Y₁Ba₂Cu₃O_7–x (YBCO) thin films. The microwave surface resistance of high quality epitaxial YBCO thin films as a function of frequencies and rf surface magnetic field H _rf was measured using the circular disk resonator technique. Using this technique the properties degradation of the resonators by edge current crowding effect was avoided. The measured R _s values are divided into three regions. In the low field region (H _rf H _c1J), R _s is independent of H _rf. In the intermediate H _rf region, R _s can be well fitted to the formula of R _s(H _rf) = a(f) + b(f) H _rf ², and b(f) is proportional to f ². This form of microwave surface resistance quantitatively agrees with the modified coupled-grain model with the idea that the materials are composed of identical superconducting grains coupled together by identical intergranular regions that function as Josephson junctions. The experimental results show that the loss mechanisms are extrinsic properties resulting from defects in the films.     

Growth and Properties of Double-Sided YBCO Films Deposited by Off-Axis Sputtering for Microwave Applications

The double-sided YBa₂Cu₃O _y (YBCO) films were grown on LaAlO₃ (LAO) substrates by an off-axis magnetron sputtering system with two 2-inch sputtering guns. High-quality YBCO films within a 50-mm-diameter area were obtained. The homogeneous YBCO films revealed transition temperature T _c(R=0) of 86K and a critical current density J _c (zero field) of 1.5×10⁶ A/cm² at 77 K. Thesurface impedance of YBCO films was measured using a probe-coupling type microstripline resonator method. The surface resistance R _S of 1.8 was obtained at 77 K around 2180 MHz. Additionally, a HTS three pole bandpass filter was fabricated and revealed a good microwave characteristic. The influence of surface roughness on microwave properties of YBCO films was discussed.