Surface impedance measurements of cuprate superconductors: Nd1.85.85Ce0.15CuO4?δ—A case study

We present results on the temperature dependence of the surface impedance of high-quality thin films and single crystals of the electron-doped Nd_1.85Ce_0.15CuO_4– cuprate superconductor. Surprisingly, these measurements are consistent with the behavior of ans-wave BCS superconductor. We also briefly review some highlights of surface impedance measurements on hole-doped cuprate superconductors, and contrast those with the results on Nd,_1.85Ce_0.15CuO_4–.     

Weak Coupling Theory of Clean (d+s)-Wave Superconductors

The properties of weakly coupled clean anisotropic (orthorhombic) superconductors with pure d and (d+s) pairing symmetry are considered. We derive analytical and universal results for generalized BCS-Mühlschlegel parameters like the zero temperature gap and the specific heat discontinuity at the transition even for the most general situation of (d+s) pairing symmetry. The properties of the gas of thermal excitations, the Bogoliubov quasiparticles, is studied through the temperature dependence of the quasiparticle entropy _B ⁰ (T), the specific heat C_B(T), the spin susceptibility _B(T), and the quasiparticle contribution K _B(T) to the electronic supercurrent response (magnetic field penetration depth). In particular we present analytical results for these quantities in the asymptotic low temperature limit T0. The experimental relevance of these results for hole-doped cuprate superconductors with orthorhombic crystal symmetry is discussed.     

Weak-link behavior in superconducting thick films

The surface impedance of melt-processed thick films of YBa₂Cu₃O_7–x on yttria-stabilized zirconia substrates has been measured as a function of temperature over the frequency range 9–18 GHz using an endwall replacement technique. The temperature dependence of both the penetration depth and the surface resistance of thisp-type cuprate system can be described within a two-gap weak-link model. The surface resistance scaled to 10 GHz by the observedf ² frequency dependence gives a value of 1.8 m at 77 K, which compares favorably with the lowest reported values for thick films of this material at microwave frequencies. Trends in material processing indicate that increasing the grain size would further decrease the surface resistance at microwave frequencies.     

Magnetic penetration depth measurements with the microstrip resonator technique

The microstrip resonator technique is a convenient way to sensitively measure the temperature dependence of the magnetic penetration depth (T) in superconducting thin films. Because the method relies on measuring the resonant frequency of a high-Q transmission line resonator at microwave frequencies, one can very precisely measure small changes in (T). This technique is applied to studying the low-temperature dependence of (T), since that is in principle a measure of the low-lying pair-breaking excitations of the superconductor. We find that the penetration depth in niobium films is consistent with the predictions of weak coupled BCS theory. The low-temperature dependence of (T) inc-axis YBa₂Cu₃O_7– films can be interpreted as either a weak exponential or as a power law. In addition, the measured value of (0) is found to be strongly dependent on the form of the temperature dependence for (T) used in fitting the data. Best fits over the entire temperature range are obtained with a BCS temperature dependence having values for 2(0)/k _BT_c strictly less than 3.5, consistent with our measurements of the temperature dependence of (T) at low temperatures in YBa₂Cu₃O_7– .     

Systematic investigation of electronic structure in BEDT-TTF based organic superconductors withTc above 10 K; κ-(BEDT-TTF)2X (X=Cu(NCS)2, Cu[N(CN)2]Br, and Cu(CN)[N(CN)2])

The electronic structure of the title superconductors has been investigated by electrical resistivity, complex susceptibility, and electron paramagnetic resonance (EPR) measurements. The superconducting properties (pressure dependence ofT _c , magnetic penetration depth, upper critical field, and so on) of these three salts are similar to each other, while transport properties in the normal state have shown a large variety in the temperature dependence. In order to clarify the electronic structure in the normal state, the EPR parameters, the spin susceptibility ( _spin), and the linewidth (H _pp), are compared. An anomalous temperature dependence of theg-value has been observed below 150 K in the Cu(NCS)₂ and Cu(CN)[N(CN)₂] salts.     

Cuprate superconductors: Universal properties and trends; evidence for Bose-Einstein condensation?

We explore the compatibility of empirical trends in various thermodynamic properties of cuprate superconductors with the Bose-Einstein condensation scenario. These trends include the relations between transition temperature, hole concentration and condensate density, the rise and the upper limit of the transition temperature, the dependence of pressure and isotope coefficients on transition temperature, as well as the observed critical behavior, which is reminiscent of three-dimensional systems with a scalar complex order parameter and short-range interactions. For this purpose we consider an interacting charged Bose gas. Due to the high polarizability of the cuprates, the Coulomb interaction is strongly screened. For this reason, the problem of calculating thermodynamic properties becomes essentially equivalent to that of the uncharged gas with short-range interactions. This problem, however, has not been solved either. Nevertheless, in the dilute limit the problem reduces to the ideal Bose gas treated by Schafroth, while in the dense regime condensation and superfluidity are suppressed because bosons of finite extension fill the available volume. This limiting behavior provides an interpolation scheme for the dependence of both transition temperature and zero temperature superfluid density on boson density. On this basis, and relating the hole concentration in the cuprates which corresponds to the boson density and the superfluid density to the square of the inverse London penetration depth, the compatibility of the empirical trends in the cuprates with the Bose gas behavior can be verified. Our analysis reveals remarkable agreement between these trends and the corresponding Bose gas behavior. There is even strong evidence of the most striking implication of this scenario, the dependence of the transition temperature on the zero-temperature superfluid density, which resembles the outline of a fly's wing. This evidence emerges from recentSR data for Tl₂Ba₂CuO₆₊ and kinetic inductance measurements for La_2–xSr_xCuO₄ films, revealing that the penetration depths of underdoped and overdoped samples atT _c do not differ significantly. In view of this we found considerable evidence of the nature of the superconducting transition in the cuprates, without invoking any specific pairing mechanism.The authors are grateful to J. G. Bednorz, D. Baeriswyl, H. Beck, J. I. Budnick, H. Keller, K. A. Müller, Ch. Niedermeier, and J. J. Rodriguez for valuable discussions.     

Superfluid Density and Angular Dependence of the Energy Gap in Optimally Doped (BiPb)2(SrLa)2CuO6+δ

We present a muon-spin rotation study of the optimally doped cuprate superconductor (BiPb)₂(SrLa)₂ CuO_6+δ . The measured magnetic field dependence of the in-plane magnetic penetration λ _ab suggests superconductivity with a dominant d-wave order parameter. The comparison of the temperature dependence of λ _ab with calculations, assuming the angular gap symmetry as obtained from photoemission measurements, is consistent with a partial suppression of the quasi-particle weight towards the anti-nodal region of the Fermi surface. This suggests that the superconducting and the pseudogap state are dominated by different parts of the Fermi surface.     

Anisotropic superconducting state parameters of Nd-Ce-CuO and La-Sr-CuO systems

Major superconducting state parameter of high-T _c electron-doped Nd-Ce-CuO and hole-doped La-Sr-CuO systems have been estimated. The analysis is based on the electronic energy band structure (EEBS) within the local density approximation. Anisotropy of the layered structure is well reflected in the shape of open Fermi surface. Determination of the effective mass of the charge carrier from the Fermi velocity using EEBS and estimates of the anisotropic superconducting state parameters, particularly the magnetic penetration depth ( _L), lead to smaller values than those observed by muon spin relaxation (SR) measurements on polycrystalline samples. The coherence length ( and ) is evaluated and appears to be higher. The temperature dependence of the Ginzburg-Landau parameter (K) and along the plane magnetic penetration depth ( _L ) shows the same nature as those revealed from experiments. Furthermore, results on lower and upper critical magnetic field are also presented. The results based on EEBS studies are consistent but do not agree well with experiments. On the other hand, if the Fermi Liquid approach (FLA) parameters are used for this analysis, the results are in better agreement with those reported earlier. The implications of the above investigations are discussed.     

Magnetic field effects in thick proximity-induced superconductors

Low-field magnetic screening and breakdown fields have been measured in thick proximity-induced superconducting copper by means of dc magnetization and ac susceptibility in the temperature range 10 to 0.005 K. From the thickness and temperature dependence of the breakdown field the Cooper pair penetration depth in copper is obtained. This value isK _N ^–1 =0.6/T m, withT in kelvins. No saturation effects were observed in the screening length , the breakdown fieldH _b, or the supercooled fieldH _sc down to the lowest temperatures.     

Power-Dependent Impedance of High Temperature Superconductor Thin Films: Relation to Harmonic Generation

We present measurements of the power-dependent microwave surface impedance of YBa₂Cu₃O_7– thin films, performed using patterned coplanar waveguide (CPW) resonators at 5.87 GHz and 76 K. We compare these resonator measurements with third-harmonic generation measurements performed on CPW transmission lines of the same geometry patterned onto the same thin-film sample at the same frequency and temperature. We find that the power-dependent surface reactance X_s(P_rf) is directly related to the magnitude of the generated third-harmonic signal, indicating a common origin for both of these manifestations of nonlinearity in high temperature superconductor (HTS) devices. These results are consistent with the nonlinear response generated by a current-dependent penetration depth (J), which provides a material limitation on the linearity that can be achieved in any practical HTS microwave device.     

Critical fields and generalized Ginzburg-Landau parameters for Mo-Re alloys containing paramagnetic impurities

We have investigated the temperature dependence of the upper critical fieldH _c2 and the thermodynamical fieldH _c for superconducting Mo-Re alloys containing magnetic impurities. In addition, the temperature dependence of the Ginzburg-Landau parameters ₁(T) and ₂(T) has been determined by measuring the magnetization and the specific heat. Our findings are compared with the theory of Fulde and Maki. In agreement with theory, our measurements show that the two pair-breaking mechanisms involved (magnetic field and magnetic impurities) are nonadditive if one departs from the linearized Ginzburg-Landau equation.     

Asymmetry between flux penetration and flux expulsion in Tl-2212 superconductors

dc magnetic hysteresis as well as flux penetration and flux expulsion were investigated in Tl_2–y Ba₂CaCu₂O_8–x polycrystals and monocrystals. All measurements were performed at 35 K and in the 0–5 T field range. Hysteresis measurements revealed an irreversibility field of about 2 T. Existing models predict identical field-cooled (fc) and zero-field-cooled (zfc) magnetizations and vanishing time dependence above this field. Although the identical fc and zfc magnetizations are in fact observed, the time dependence vanishes only for flux penetration after zero-field cooling; a remanence is preserved after field cooling and decays with a finite relaxation rate. Activation energies calculated on the basis of the thermal activation model display a pronounced field dependence, and arelower for flux penetration than for flux expulsion in high fields (H3 T) for all orientations. This behavior of extreme layered superconductors contradicts classical theoretical models and questions the original definition of the irreversibility line as well. All of our results are consistent with the recent theory of lock-in transition, and can be well interpreted by using those principles.     

Temperature dependence of Nb penetration depth measured by a resistive method

Besides the conventional method of measuring the penetration depth of Nb superconductors in Nb/AlO_x/Nb Josephson junction, a simple resistive method is applied in this study. With the applied magnetic field parallel to the junction plane, resistive measurement of resistance–temperature characteristics in a given magnetic field or resistance–magnetic field curves at a fixed temperature show resistance peaks whenever the total magnetic flux through the junction equals an integral multiple of the flux quantum. We demonstrate how to determine the penetration depth from such measurements and discuss its temperature dependence in terms of fundamental film properties.     

Single-Crystal Growth and Anisotropy of the Tetragonal 1-2-3 Type Superconductor Ca0.5La1.25Ba1.25Cu3Oy

Single crystals of the tetragonal 1-2-3 type cuprate Ca_0.5La_1.25Ba_1.25Cu₃Oy have been grown by the travelling-solvent floating-zone method. The crystal structure has been determined to belong to the tetragonal P4/mmm by the single-crystal x-ray diffraction for several crystals with different oxygen-contents. The superconducting transition temperature T _c has increased up to 75 K by the annealing in 1000 bar of O₂. Temperature dependences of the resistivities _ab , _c and also the angular dependence of _ab in various constant magnetic fields have been measured. The anisotropic parameter has been estimated as 6.2, which is similar to that of YBa₂Cu₃O₇.     

Spin-Injection Quasiparticle Nonequilibrium in Cuprate/Manganite Heterostructures

Quasiparticle nonequilibrium due to spin-polarized current injection in perovskite superconductor/ferromagnet (S/F) thin-film heterostructures has been studied with the technique of cryogenic scanning tunneling spectroscopy. The spin-injection heterostructures consisted of epitaxial bilayers of the high-T _c superconductor YBa₂Cu₃O_{7 –} and the half-metallic ferromagnet La_0.7Ca_0.3MnO₃, with a spin-polarized quasiparticle current injected into the cuprate layer from the manganite layer. The tunneling conductance measured at 4.2 K on the cuprate layer showed a distinctly nonequilibrium quasiparticle spectrum as a result of the spin injection. Quantitative analysis of the tunneling spectral evolution versus the injection current yielded an estimate of the quasiparticle spin-diffusion depth and the spin-relaxation time in the superconducting cuprate.     

Magnetic Interaction in Insulating Cuprates

We examine two-spin (2S) and cyclic four-spin (4S) magnetic interactions in insulating ladder and two-dimensional (2D) cuprates. By a comparison of eigenstates between d-p and Heisenberg models, we evaluate magnitudes of these interactions. We find that the 4S interaction is 10 % of nearest neighboring 2S interaction, and a diagonal 2S interaction is considerably small. The 4S interaction for a ladder cuprate is larger than that for 2D one, and plays an important role in the low-energy excitation. The Heisenberg ladder with the obtained 2S and 4S interactions reproduces very well the experimental result of the temperature dependence of the magnetic susceptibility.     

The superconducting state of YBa2Cu3O7−δ

Many low temperature properties of high T_c superconductors deviate significantly from the detailed predictions of BCS theory. Here we discuss whether these effects could be caused by either: (a) an unconventional pairing state, or (b) local randomness in the gap function due to the intrinsic disorder. We review recent experiments pertinent to these questions: Josephson effects in (001) oriented planar junctions between YBa₂Cu₃O₇- and classic superconductors and the temperature dependence of the a-b plane electro-magnetic penetration depth at low temperatures. We also calculate the density of states of s-wave superconductors with local quenched disorder in the gap function so as to determine whether s-wave pairing could be consistent with the low energy quasiparticle excitations seen in many experiments.     

Low-Field microwave measurements of YBa2Cu3O7?x near the superconducting transition temperature

Novel microwave absorption and dispersion measurements have been performed on well-characterized single-crystal platelets of the high-T _c superconductor YBa₂Cu₃O_7–x . The results are explained in terms of the rapid variation of the penetration depth near and belowT _c . Since EPR measurements are very sensitive to small changes in absorption and dispersion, this technique should be very useful in the understanding of the transition temperature region in both new and old superconducting materials.