Angular dependence of the critical magnetic field in granular superconducting films

The critical magnetic fieldH _c () of granular Al films has been measured as a function of the angle between the field direction and the plane of the film at temperatures nearT _c0 .The film thicknessd is smaller than the temperature-dependent coherence length (T), the bulk electron mean free path1 is smaller than the BCS coherence length ₀, and 1 d. The experimental data onH _c () are well fitted by the Tinkham formula. However, the observed values ofH _c/H _care not always consistent with and increase with1/d. This fact suggests that the boundary scattering of electrons at the film surface enhancesH _c () and that the enhancement ofH _cis larger than that ofH _c.On leave from Department of Physics, Faculty of Science, Kyushu University, Fukuoka, Japan.     

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– .     

Heat conduction in Ba1?xKxBiO3

We have investigated heat conduction of single crystal Ba_1–xK_xBiO₃ in the temperature range of 2–300 K and in a magnetic field of up to 6 Tesla. Temperature dependence of thermal conductivity(T) reveals the participation of both electrons and phonons with their relative contributions that depend critically on the potassium doping concentration. Crystals underdoped with potassium (samples with higherT _c) exhibit a strong suppression of and a glass-like temperature dependence. In contrast, those with a higher potassium content (lowerT _c) show an increase as temperature decreases with a peak near 23 K. Field dependence of(H) is also very sensitive to the level of potassium doping. Crystals exhibiting a large phonon contribution show an initial drop in(H) at low fields followed by a minimum and then a slow rise to saturation as the field increases. The initial drop is due to the additional phonon scattering by magnetic vortices as the sample enters a mixed state. The high field behavior of(H), arising from a continuous break-up of Cooper pairs, exhibits scaling which suggests the presence of an unconventional superconducting gap structure in this material.     

Anisotropy effects in tantalum,niobium, and vanadium down to the millikelvin temperature range

Experiments on the transition fields to the normal conducting state were made on single crystals of Ta, Nb, and V in the temperature range between 40 mK and the transition temperature. In tantalum results are presented on the thermodynamic quantitiesT _c, ₀ H _c(T),D(t), and in the clean limit and as a function of impurity concentration at low impurity levels (<0.15 at %). Special attention is paid to the phase transition between type I and type II superconductivity, which occurs at a certain conversion temperatureT* _c in materials with (T _c)<1/2. This transition is found to be strongly anisotropic because of theH _c2 anisotropy effect appearing in the type II superconducting state. It is shown that atT=0 no signs of type II superconductivity will appear for (T _c)0.44, whereas type II superconductivity will be found in every crystal direction for (T _c)0.50. The analysis ofH _c2 anisotropy in Ta in terms of cubic harmonic functions demonstrates that the first anisotropic expansion coefficienta ₄ remains finite atT*, whereas the second,a ₆, vanishes when type II superconductivity disappears. No significant values of any higher order coefficient could be detected in Ta. For Nb and V the temperature dependence of the anisotropy coefficientsa ₄,a ₆,a ₈, anda ₁₀ was established in the entire temperature range. The diversity of results clearly indicates that different microscopic mechanisms contribute to the observedH _c2 anisotropy effect in these materials.     

Hall-Effect study of YNi2B2C superconductor

Hall-effect and critical magnetic fields H_c2(T) have been studied for YNi₂B₂C (prepared using high pressure technique) at H130 kOe and 1.6T300K. The normal state Hall coefficient R_H was found to be negative (R_H=–1.43.10^–11 cm/Oe at T=4.2 K and H=130 kOe) and slightly growing in absolute value with increase of temperature. The dependence of the Hall voltage on magnetic field in the mixed superconducting state shows no sign reversal as was observed earlier for some high-T_c systems. The values of ¦H_c2/ T¦and H_c2(0) are found to be 4.8 kOe/K and 47 kOe respectively.     

Voltage-current characteristics of a type-II superconductor placed in a transverse magnetic field

We have measured the voltageV appearing along a type-II superconducting sample carrying a longitudinal currentI in the presence of a transverse magnetic fieldH. The analysis of the nonlinear part ofV(I) curves does not verify the recent model of Sherrill and Payne. The linear part ofV(I) curves shows that the flux-flow resistivity _f is exponential inH nearH _c2, as Axt and Joiner found. We estimated the parameter =(H _c2/_n)(d_f/dH)_{H=H c2} as a function of the reduced temperature and have compared it to some of the existing theories.     

Quantum oscillations and reversible and irreversible superconducting phase transitions in indium microcylinders

Using a sensitive mutual inductance method, measurements of first- and second-order phase transitions in indium microcylinders (2.8–7.6 µm in diameter) have been made. Quantum oscillations in the supercooling field have been observed. The values of _SC (T/T _c )=₁(T/T _c ) derived fromH _SC =H _C3 have been corrected for both the temperature and the size dependence in the relationship betweenH _c2 andH _c3 . The results for ₁(T/T _c ) from the 7.6-µm sample then agree reasonably well with the temperature dependence of ₁ observed for niobium. However, for the smallest cylinders anomalously low values of _SC (T/T _c ) were obtained nearT _c . Very close to the transition temperature second-order (nonhysteretic) phase transitions have been observed and are interpreted in terms of the Ginzburg-Landau theory.     

Effect of phase fluctuations upon penetration depth

The temperature dependence of the static penetration (T) has been used as a guide to the nature of the superconducting state in high-T _c materials. It has been argued that an algebraic temperature dependence in the ratio (T)/(0) [(T) — (0)]/(0) at low temperature is evidence for d-wave pairing. This paper examines the effect of superconducting phase fluctuations upon (T) and finds an algebraic dependence over a broad range of temperature.     

Critical light scattering in4He near the gas-liquid critical point

Scattered intensities of light were measured near the gas-liquid critical point of ⁴ He at scattering angles of 30, 60, and 90° as functions of the reduced temperature =|T–T _c |/T _c along the critical isochore (T>T _c ) and the coexistence curve (T>T _c ). The temperature range was 3×10 ^–5 <<1.5×10 ^–2 . Critical exponents and coefficients describing divergence of the generalized susceptibility and the correlation length are obtained as (T>T _c )=1.31±0.02, v(T>T _c )=0.66±0.02, ₀ (T>T _c )=4.2±0.6 Å, (T>T _c )=1.32±0.02, v(T>T _c )=0.68±0.02, _± (T>T _c )=2.6±0.7 Å, =0.06±0.06(T>T _c ), 0.05±0.05(T>T _c ), and ₀(T>T _c )/x_± (T>T _c )=3.6±0.4. It is pointed out that the quantal nature of ⁴ He has remarkable influence on the critical behavior of ⁴ He in the above-mentioned temperature region.     

d-Hole localization and the suppression of superconductivity in YBa2(Cu1-xZnx)3O7?y

The temperature and Zn concentration dependence of the electrical resistivity, specific heat, magnetic susceptibility, and electron paramagnetic resonance (EPR) spectra of YBa₂(Cu_1–x Zn _x )₃O_7–y withy0.1 has been measured forx0.16. In addition, the temperature and field dependence of the magnetization has been measured for 2<T<300K and 0<H<9.0T, along with the temperature and quasihydrostatic pressure dependence of the electrical resistivity for selected samples for 0<P<13 GPa. The substitution of Zn for Cu in YBa₂Cu₃O_7–y causes a rapid and nearly linear depression of the superconducting transition temperature,T _c , withT _c going to 0 K forx 0.10. YBa₂(Cu_1–x Zn _x )₃O_7–y retains the YBa₂Cu₃O_7-y orthorhombic structure forx0.16 for both the superconducting and nonsuperconducting samples. Initially, the unit cell volume increases nearly linearly with Zn content; however, an abrupt change occurs in the vicinityx=0.8–0.10. Forx<0.10, the temperature dependence of the electrical resistivity,(T), is metallic-like (d/dT>0) and increases gradually with increasing Zn content. However, forx 0.10,(T) becomes semiconductor-like, with a very rapid increase of the resistivity with increasingx. The electrical resistivity, magnetic susceptibility, EPR spectra, and specific heat all indicate that thed-holes associated with the Cu ions become localized in the nonsuperconducting phase,x>-0.10.     

Kondo effect and impurity interactions in the resistivity of diluteZnMn alloys

The electrical resistivity of diluteZnMn alloys (c=1.7–2400 ppm Mn) has been investigated in the temperature range from 0.05 to 14 K. For the most dilute sample, single-impurity Kondo behavior is found, well described by the Hamann formula withT _K=0.9 K,S=3/2. ForT<50 mK, aT ² law with _R =0.3 K is expected. In the dilute limit the Kondo slope is –(1/c)d()/d(logT)=3.7±0.2 µ-cm/at % dec. In the more highly concentrated alloys, the slope decreases with increasing c and the lnT-like variation of the Kondo resistivity roughly terminates near a temperatureT _W(c),T _W being related to the average Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction strength between the Mn impurities. For 20 ppm c 1000 ppm, the resistivity slightly decreases at low temperatures and a broad resistivity maximum is observed atT _m (c), withT _m c ^0.7. ForT 2 _m, the resistivity dependence is linear inT, and for the most concentrated alloy aT ^3/2 orT ² dependence is measured at the lowest temperatures attainable. The investigation of the transition temperatureT _c (c) to superconductivity ofZnMn results in a critical concentrationc _cr=18 ppm Mn. The concentration dependence ofT _c below 0.3 K suggests the presence of the Kondo effect, although impurity interactions may also influenceT _c in this temperature range.Supported by Deutsche Forschungsgemeinschaft.     

Upper Critical Field Hc2 on c Axis of Ag/Bi-2223 Polycrystal Tape

The upper critical field H _c2, based on Ginzburg–Landau theory at medial magnetic fields, can be calculated from the relationship of the magnetization intensity M(H) versus magnetic field H if M is linear with ln₀ H. For Ag/Bi-2223 tapes, the measured M(H) was found to be linear with ln₀ H. In this case, the values of H _c2(T) may in principle be determined. To do this, we will meet another problem in that the obliquity of crystal planes is not equal for different grains in tapes, and values of grain-oblique angle will appear in the calculated H _c2. Obviously, for Ag/Bi-2223 tapes is an uncertain parameter and hard to determine. To avoid the effects of , we only study the H _c2 in the c axis direction and the projections of H onto the c axis is taken as the actual applied fields. Thus, the effects of grain-oblique angle may be counteracted when measuring critical current density J, if the external magnetic fields are applied to the tape along both the parallel to and perpendicular to the c axes directions (on the narrow surfaces of the tape). On medial fields (H = 0 – 3 T), the upper critical fields H _c2(T) on c axis for the Ag/Bi-2223 tape are obtained and fitted as ₀ H _c2(T) = 830 e ^–0.07T . The average slope d[₀ H _c2(T)]/dT – 8T/K is found to be as large as that of Bi-2212. On extrapolating the relation to T = 0 K, the value of ₀ H _c2(0) 800T. The coherence length _ab is determined from H _c2(c), and _ab (0) = 0.63 nm at T = 0 K.     

Scaling Behavior and Estimation of Activation Energy of Polycrystalline RuSr2GdCu2O8 Superconductor from AC Susceptibility Measurements

In this study, the measured curves of AC susceptibility (ACS) components, (T) and (T), of polycrystalline RuSr₂GdCu₂O₈ (Ru-1212) superconductor were scaled onto a single curve using the peak temperature of its imaginary part (T _p) as the scaling parameter for various AC field amplitudes from 0.5 to 24 G. The dependence of the AC magnetic field amplitude on T _p is scaled as: H _ac (1–T _p/T _c)^2.25. Similarly, the current density J _c, extracted from the AC field amplitude is also scaled as: J _c (1 – T _p/T _c)^2.25. The dependencies of T _p on frequency and AC field amplitude are also investigated and the time parameter t ₀ of the order of 10^–8 s is estimated from the dependence of T _p on frequency. The dependencies of activation energy on temperature, T, and the field amplitude, H _ac, are obtained from the Arrhenius-like semilog plot of frequency () and T _p. Such dependencies on temperature and field amplitude can be described by a scaling law of the form: U(H _ac,T) = U ₀[1 – T/T _p]H _ac ^–0.17.     

Non fermi liquid ground states in strongly correlated f-electron materials

Experimental efforts to characterize and develop an understanding of non Fermi liquid (NFL) behavior at low temperature in f-electron materials are reviewed for three f-electron systems: M_1–xU_xPd₃ (M = Sc, Y), U_1–xTh_xPd₂Al₃, and UCu_5–xPd_x. The emerging systematics of NFL behavior in f-electron systems, based on the present sample of nearly ten f-electron systems, is updated. Many of the f-electron systems exhibit the following temperature dependences of the electrical resistivity p, specific heat C, and magnetic susceptibility for T T₀, where T_o is a characteristic temperature: P(T) 1 –aT/T ₀, where a < 0 or > 0, C(T)/T (-1/T _o) In (T/bT ₀), and (T) 1 –c(T/T_o)^1/2. In several of the f-electron systems, the characteristic temperature T_o can be identified with the Kondo temperature T_k.     

Quantum fluctuations in continuous superconducting films

Motivated by recent experiments on ultrathin continuous superconducting films, we study the dependence ofT _c and (for zero temperatures) on the film thicknessd. Using field-theoretical methods, we express the Coulomb interaction in terms of a fluctuating potential, and the fluctuation correction to the free energy (in one-loop approximation) is determined. Based on the standard dirty-limit expressions for the response functions, we findT _c and by a numerical investigation of the gap equation. Generally, we find that the decrease ofT _c and vs.d ^–1 is quite similar, but depends sensitively on both the large-wave-vector cut-off and the strength of the interaction. In particular, however, for a strong interaction (Coulomb interaction), the order parameter is more strongly suppressed than the critical temperature, which is due to long-wavelength fluctuations of the phase and the potential.     

The transverse acoustic impedance of dilute solutions of3He in superfluid4He

The transverse acoustic impedanceZ=R–iX of dilute solutions of³He in superfluid⁴He has been measured at a frequency (/2) of 20.5 MHz at temperaturesT from 30 mK to the transition at T. The³He concentrations studied werec=0.014, 0.031, 0.053, 0.060, and 0.092 below 1 K, thoughc decreased slightly near the point. The impedance was found from the temperature dependence of the quality factor and the resonant frequency of anAT-cut quartz crystal resonator immersed in the liquid. Below 1 K,Z is due to the Fermi gas of³He quasiparticles, and in the collisionless limit, 1 ( is a relaxation time),R remains constant whileX goes to zero. Measurements ofR(c, T) andX(c, T) were analyzed to determine the momentum accommodation coefficient (c, T) and (c, T). The relaxation times were in good agreement with previous work, while (c, T) was independent ofc, but increased from 0.29±0.03 below 0.1 K to 1.0±0.1 above 0.8 K. Various mechanisms are suggested to explain this. Between 1.0 and 1.5 K the³He quasiparticles and the thermally excited rotons are in the hydrodynamic region, 1. Values of the total viscosity (c, T) were obtained and analyzed to give the³He gas viscosity and the³He-³He and roton-³He scattering rates, both of which were energy-dependent. The superfluid healing length a was also measured. Near the point we founda=(0.1±0.03)^–2/3 nm, where =1–T/T, proportional to the phase coherence length . Our data are consistent with the hypothesis that _s/T is a universal constant for superfluid dilute solutions, where _s is the superfluid density. Between 1.0 and 1.8 K we found thata(c, T) was comparable to measurements in³He-⁴He films.     

Thermal conductivity of superconducting UPt3

The thermal conductivity of the heavy-fermion superconductor UPt₃ has been measured on two single crystals of different quality as a function of temperature and applied magnetic field for different orientations of the heat current relative to both the field and the crystalline axes. The temperature dependence of is far from exponential and nearly the same for both crystals, in which the heat current is, respectively, parallel and perpendicular to the hexagonalc axis, suggesting a gap structure with nodes in the basal plane and normal to it. The field dependence of is strongly anisotropic. In the best sample at low fields, where the scattering of heat carriers by vortices is thought to be important, (H) depends on the relative orientation of field and current. On the other hand, at high fields nearH _c2 (in both samples), (H) depends on the relative orientation of field and crystalline axes, reflecting an anisotropy in the gap structure and in the Fermi velocities.     

On the analysis of tunneling data for A15 superconductors

We examine the applicability of the standard McMillan inversion of Eliashberg's equations for superconductors with a nonconstant electronic density of statesN(). We do this usign simple models forN() and a realistically shapedN() taken from recent band structure work for Nb₃Sn. It turns out that peak structure inN() near _F may lead to gross errors in the derived Eliashberg function ²F() when the energy dependence ofN() is omitted in the inversion procedure. For Nb₃Sn, this leads to a 40% overestimate of when ²F() is evaluated via the standard McMillan program.     

Microwave surface resistance of epitaxial YBa2Cu3O7 thin films at 18.7 GHz measured by a dielectric resonator technique

We used a dielectric resonator technique for highly sensitive measurements of the temperature dependence of the microwave surface resistanceR _s of 1×1 cm² superconducting films at 18.7 GHz. It consists of a sapphire disc positioned on the film under investigation within a copper cavity which is acting as a radiation shield. In the TE₀₁ oscillation mode the highly reproducible quality factor of about 10⁵ results in a sensitivity of ±50 forR _s measurements. The temperature dependence ofR _s can be measured up to values as high as 1 . We have investigated several YBa₂Cu₃O₇ thin films prepared by high oxygen pressure d.c. sputtering on LaAlO₃ and NdGaO₃. Our best films exhibit a pronounced nonlinear behavior of the d.c. resistivity(T) with(300K)/(100K) values of about 3.7. Those films show, besides the initial fall-off just belowT _c , a further strong decrease ofR _s at low temperatures. This was observed both at 18.7 GHz and 87 GHz, as measured by a conventional cavity end plate replacement technique. ForTT_c/2 these films exhibit an exp (–T _c/T) dependence ofR _s with-values around 0.4. These observations may be explained by a superconducting energy gap with 2/kT _c0.8 for charge carriers localized in the CuO chains for YBa₂Cu₃O₇.     

Flux flow resistivity of superconducting thin film

The flux flow resistivity _f has been investigated in the range of reduced temperature 0.5–0.99 for indium thin films having the properties of dirty, type II superconductors. In this temperature range _f was found to show a linear dependence on magnetic field strength for low values of the field. The temperature-dependent viscosity coefficient of the flux flow was obtained and compared with the microscopic theories of Gor'kov and Kopnin (GK) and others. Reasonable agreement with the GK theory was obtained except in the vicinity ofT _c. NearT _c, the viscosity coefficient [in units of ₀H_c(t)_n ^–1c^–2] showed a remarkable decrease beyond a maximum, contrary to the theoretical prediction. Although this behavior is not yet well understood, it seemed to appear asd/ became small. The nonlinearity of the current(I)-voltage(V) curves is also discussed. It was found that a linearI–V curve is found only in the region of temperature and magnetic field where the conditionI _p<1/10I_c is satisfied, whereI _p is the depinning current andI _c is the effective critical current. In the measurements the temperature rise of the film specimens was recorded and the effect due to thermal heating of the specimens was estimated.On leave from Department of Electronic Engineering, Faculty of Engineering, Kyushu Industrial University, Fukuoka, Japan.