Probing the superconducting gap symmetry of PrOs4Sb12: a penetration depth study

We report measurements of the magnetic penetration depth lambda in single crystals of PrOs4Sb12 down to 0.1 K, with the ac field applied along the a, b, and c directions. In all three field orientations, lambda approximately T2 and superfluid density rho(s) approximately T2 for T<0.3T(c). Data are best fit by the 3He A-phase-like gap with multidomains, each having two point nodes along a cube axis, and parameter Delta(0)(0)/k(B)T(c)=2.6, suggesting that PrOs4Sb12 is a strong-coupling superconductor with two point nodes on the Fermi surface. We also confirm the double transitions at 1.75 and 1.85 K seen in other measurements.     

Muon-spin-rotation measurements of the penetration depth of the infinite-layer electron-doped Sr0.9La0.1CuO2 cuprate superconductor

Muon-spin-rotation (muSR) measurements of the in-plane penetration depth lambda(ab) have been performed in the infinite-layer electron-doped Sr0.9La0.1CuO2 high-T(c) superconductor (HTS). Absence of the magnetic rare-earth ions in this compound allowed us to measure for the first time the absolute value of lambda(ab)(0) in electron-doped HTSs using muSR. We found lambda(ab)(0)=116(2) nm. The zero-temperature depolarization rate sigma(0) proportional, variant 1/lambda(2)(ab)(0)=4.6(1) micros(-1) is more than 4 times higher than expected from the Uemura line. Therefore, this electron-doped HTS does not follow the Uemura relation found for hole-doped HTSs.     

Effect of pressure on the Ginzburg-Landau parameter kappa=lambda/xi in YB6

Measurements of the transition temperature Tc, the upper critical field Hc2, and the magnetic penetration depth lambda under hydrostatic pressure (up to approximately 9.2 kbar) in the YB6 superconductor were carried out. A pronounced and negative pressure effect (PE) on Tc and Hc2 with dTc/dp=-0.0547(4) K/kbar and micro0dHc2(0)/dp=-4.84(20) mT/kbar, and zero PE on lambda(0) were observed. The PE on the coherence length dxi(0)/dp=0.28(2) nm/kbar was calculated from the measured pressure dependence of Hc2(0). Together with the zero PE on the magnetic penetration depth lambda(0), our results imply that the Ginzburg-Landau parameter kappa(0)=xi(0)/lambda(0) depends on pressure and that pressure "softens" YB6, e.g., moves it to the type-I direction.     

Pronounced enhancement of the lower critical field and critical current deep in the superconducting state of PrOs4Sb12

We have observed an unexpected enhancement of the lower critical field H(c1)(T) and the critical current I(c)(T) deep in the superconducting state below T approximately 0.6 K (T/T(c) approximately 0.3) in the filled skutterudite heavy fermion superconductor PrOs(4)Sb(12). From a comparison of the behavior of H(c1)(T) with that of the heavy fermion superconductors U(1-x)Th(x)Be(13) and UPt(3), we speculate that the enhancement of H(c1)(T) and I(c)(T) in PrOs(4)Sb(12) reflects a transition into another superconducting phase that occurs below T/T(c) approximately 0.3. An examination of the literature reveals unexplained anomalies in other physical properties of PrOs(4)Sb(12) near T/T(c) approximately 0.3 that correlate with the features we have observed in H(c1)(T) and I(c)(T).     

Evidence for unconventional strong-coupling superconductivity in PrOs4Sb12: an Sb nuclear quadrupole resonance study

We report Sb-NQR results which evidence a heavy-fermion (HF) behavior and an unconventional superconducting (SC) property in Pr(Os4Sb12 with T(c)=1.85 K. The temperature (T) dependence of nuclear-spin-lattice-relaxation rate, 1/T(1), and NQR frequency unravel a low-lying crystal-electric-field splitting below T0 approximately 10 K, associated with Pr3+(4f(2))-derived ground state. In the SC state, 1/T(1) shows neither a coherence peak just below T(c) K nor a T3-like power-law behavior observed for anisotropic HF superconductors with the line-node gap. The isotropic energy gap with its size Delta/k(B)=4.8 K seems to open up across T(c) below T(*) approximately 2.3 K. It is surprising that Pr(Os4Sb12 looks like an isotropic HF superconductor-it may indeed argue for Cooper pairing via quadrupolar fluctuations.     

Pressure effects on the transition temperature and the magnetic field penetration depth in the pyrochlore superconductor RbOs2O6

Magnetization measurements under hydrostatic pressure up to 8 kbar in the pyrochlore superconductor RbOs2O6 (T(c) approximately or equal 6.3 K at p=0) were carried out. A positive pressure effect on T(c) with dT(c)/dp=0.090(3) K/kbar was observed, whereas no pressure effect on the magnetic penetration depth lambda was detected. The pressure independent ratio 2 Delta(0)/k(B)T(c)=3.72(2) (Delta(0) is the superconducting gap at zero temperature) was found to be close to the BCS value 3.52. Magnetization and muon-spin rotation measurements of lambda(T) indicate that RbOs2O6 is an adiabatic s-wave BCS-type superconductor. The value of lambda extrapolated to zero temperature and ambient pressure was estimated to be 230(30) nm.     

Electric-field-effect modulation of the transition temperature, mobile carrier density, and in-plane penetration depth of NdBa2Cu3O7-delta thin films

We explore the relationship between the critical temperature T(c), the mobile areal carrier density n(2D), and the zero-temperature magnetic in-plane penetration depth lambda(ab)(0) in very thin underdoped NdBa(2)Cu(3)O(7-delta) films near the superconductor to insulator transition using the electric-field-effect technique. Having established consistency with a Kosterlitz-Thouless transition, we observe that T(KT) depends linearly on n(2D), the signature of a quantum superconductor to insulator transition in two dimensions with znu(over)=1, where z is the dynamic and nu is the critical exponent of the in-plane correlation length.     

Crystal field potential of PrOs4Sb12: consequences for superconductivity

The results of inelastic neutron scattering provide a solution for the crystal field level scheme in PrOs4Sb12, in which the ground state in the cubic crystal field potential of T(h) symmetry is a Gamma(1) singlet. The conduction electron mass enhancement is consistent with inelastic exchange scattering, and we propose that inelastic quadrupolar, or aspherical Coulomb, scattering is responsible for enhancing the superconducting transition temperature. PrOs4Sb12 appears to be the first compound in which aspherical Coulomb scattering is strong enough to overcome magnetic pair breaking and increase T(c).     

Experimental evidence of s-wave superconductivity in bulk CaC6

The temperature dependence of the in-plane magnetic penetration depth, lambda(ab)(T), has been measured in a c-axis oriented polycrystalline CaC(6) bulk sample using a high-resolution mutual inductance technique. A clear exponential behavior of lambda(ab)(T) has been observed at low temperatures, strongly suggesting isotropic s-wave pairing. Data fit using the standard BCS theory yields lambda(ab)(0) = (720 +/- 80) A and delta(0) = (1.79 +/- 0.08) meV. The ratio 2delta(0)/k(B)T(c) = (3.6 +/- 0.2) gives indication for a weakly coupled superconductor.     

Coexistence of magnetic fluctuations and superconductivity in the pnictide high temperature superconductor SmFeAsO1-xFx measured by muon spin rotation

Muon spin rotation experiments were performed on the pnictide high temperature superconductor SmFeAsO1-xFx with x=0.18 and 0.3. We observed an unusual enhancement of slow spin fluctuations in the vicinity of the superconducting transition which suggests that the spin fluctuations contribute to the formation of an unconventional superconducting state. An estimate of the in-plane penetration depth lambda ab(0)=190(5) nm was obtained, which confirms that the pnictide superconductors obey an Uemura-style relationship between Tc and lambda ab(0);(-2).     

Field and temperature dependence of the superfluid density in LaFeAsO1-xFx superconductors: a muon spin relaxation study

We present zero field and transverse field muon spin relaxation experiments on the recently discovered Fe-based superconductor LaFeAsO1-xFx (x=0.075 and x=0.1). The temperature dependence of the deduced superfluid density is consistent with a BCS s-wave or a dirty d-wave gap function, while the field dependence strongly evidences unconventional superconductivity. We obtain the in-plane penetration depth of lambda ab(0)=254(2) nm for x=0.1 and lambda ab(0)=364(8) nm for x=0.075. Further evidence for unconventional superconductivity is provided by the ratio of Tc versus the superfluid density, which is close to the Uemura line of high-Tc cuprates.     

A theoretical study of tunnelling conductance in ferromagnet/ PrOs4Sb12 junctions

The tunnelling conductance spectra of ferromagnet/PrOs4Sb12 junctions are theoretically investigated by using the Blonder-Tinkham-Klapwijk theory. Three pairs of possible candidate for the pairing symmetry of superconducting energy gap of the recently discovered heavy-fermion unconventional superconductor PrOs4Sb12 are chosen for calculation. We have studied the spin-polarization effect on the conductance spectra, with respect to different strength of ferromagnetism of the ferromagnet and different strength of the interface barrier. Moreover, we have discussed the influence of nodal structures of the superconducting energy gap on the conductance spectra. Different features of the tunnelling conductance spectra were got, which may serve as useful theoretical comparisons for future experiments.     

Experimental evidence for two gaps in the high-temperature La1.83Sr0.17CuO4 superconductor

The in-plane magnetic field penetration depth (lambda(ab)) in single-crystal La1.83Sr0.17CuO4 was investigated by muon-spin rotation (muSR). The temperature dependence of lambda(ab)(-2) has an inflection point around 10-15 K, suggesting the presence of two superconducting gaps: a large gap (Delta(1)(d)) with d-wave and a small gap (Delta(2)(s)) with s-wave symmetry. The zero-temperature values of the gaps at mu(0)H=0.02 T were found to be Delta(1)(d)(0)=8.2(1) meV and Delta(2)(s)(0)=1.57(8) meV.     

Multiple superconducting phases in new heavy fermion superconductor PrOs4Sb12

The superconducting gap structure of recently discovered heavy fermion superconductor PrOs4Sb12 was investigated by using thermal transport measurements in magnetic field rotated relative to the crystal axes. We demonstrate that a novel change in the symmetry of the superconducting gap function occurs deep inside the superconducting state, giving a clear indication of the presence of two distinct superconducting phases with twofold and fourfold symmetries. We infer that the gap functions in both phases have a point node singularity, in contrast to the familiar line node singularity observed in almost all unconventional superconductors.     

Direct observation of quadrupolar excitons in the heavy-fermion superconductor PrOs4Sb12

We report inelastic neutron scattering experiments performed to investigate the low energy magnetic excitations on single crystals of the heavy-fermion superconductor PrOs(4)Sb(12). The observed excitation clearly softens at a wave vector Q=(1,0,0), which is the same as the modulation vector of the field-induced antiferro-quadrupolar ordering, and its intensity at Q=(1,0,0) is smaller than that around the zone center. This result directly evidences that this excitonic behavior is derived mainly from nonmagnetic quadrupolar interactions. Furthermore, the narrowing of the linewidths of the excitations below the superconducting transition temperature indicates the close connection between the superconductivity and the excitons.     

Free energy and torque for superconductors with different anisotropies of H(c2) and lambda

The free energy is evaluated for a uniaxial superconductor with the anisotropy of the upper critical field, gamma(H)=H(c2,a)/H(c2,c), different from the anisotropy of the penetration depth gamma(lambda)=lambda(c)/lambda(a). With increasing difference between gamma(H) and gamma(lambda), the equilibrium orientation of the crystal relative to the applied field may shift from theta=pi/2 (theta is the angle between the field and the c axis) to lower angles and reach theta=0 for large enough gamma(H). These effects are expected to take place in MgB2.     

Direct observation of the oxygen isotope effect on the in-plane magnetic field penetration depth in optimally doped YBa2Cu3O7-delta

We report the first direct observation of the oxygen-isotope ((16)O/(18)O) effect on the in-plane penetration depth lambda(ab) in a nearly optimally doped YBa(2)Cu(3)O(7-delta) film using the novel low-energy muon-spin rotation technique. Spin-polarized low-energy muons are implanted in the film at a known depth z beneath the surface and process in the local magnetic field B(z). This feature allows us to measure directly the profile B(z) of the magnetic field inside the superconducting film in the Meissner state and to make a straightforward determination of lambda(ab). A substantial isotope shift Delta lambda(ab)/lambda(ab)=2.8(1.0)% at 4 K is observed, implying that the in-plane effective supercarrier mass m*(ab) is oxygen-isotope dependent with Delta m*(ab)/m*(ab)=5.5(2.0)%. These results are in good agreement with magnetization measurements on powder samples.     

Isotropically gapped strong-coupling superconductivity in the beta-pyrochlore KOs2O6: evidence from penetration depth measurements

We report on measurements of the temperature dependence of the magnetic penetration depth down to 0.04 K in a high-quality sample of the beta-pyrochlore KOs2O6 (Tc=9.65 K) with a spin-frustrated lattice. We observe temperature-independent behavior below T approximately 0.3Tc, which is firm evidence for the presence of an isotropic superconducting gap in this material. In the whole temperature range the superfluid density is very well described, without the need of adjustable parameters, by a strong-coupling extension of the BCS model for an isotropic gap. Thus, the penetration depth results indicate that KOs2O6 is a strong-coupling superconductor with a fully developed energy gap. No effect of the second phase transition taking place at Tp=7.5 K was observed on the penetration depth, which suggests that the Cooper pairs remain unperturbed across this transition.     

Superconductivity and field-induced magnetism in Pr2-xCexCuO4 single crystals

We report muon-spin rotation and relaxation (muSR) measurements on single crystals of the electron-doped high-T(c) superconductor Pr2-xCexCuO4. In a zero external magnetic field, superconductivity is found to coexist with dilute Cu spins that are static on the muSR time scale. In an applied field, we observe a mu(+)-Knight shift that is primarily due to the magnetic moment induced on the Pr ions. Below the superconducting transition temperature T(c), an additional source of local magnetic field appears throughout the volume of the sample. This finding is shown to be consistent with field-induced antiferromagnetic ordering of the Cu spins. Measurements of the temperature dependence of the in-plane magnetic penetration depth lambda(ab) in the vortex state are also presented.     

Oxygen-isotope effect on the In-plane penetration depth in underdoped La2-xSrxCuO4 single crystals

We report measurements of the oxygen-isotope effect (OIE) on the in-plane penetration depth lambda(ab)(0) in underdoped La2-xSrxCuO4 single crystals. A highly sensitive magnetic torque sensor with a resolution of Deltatau approximately 10(-12) N m was used for the magnetic measurements on microcrystals with a mass of approximately 10 &mgr;g. The OIE on lambda(-2)(ab)(0) is found to be -10(2)% for x = 0.080 and -8(1)% for x = 0.086. It arises mainly from the oxygen-mass dependence of the in-plane effective mass m(*)(ab). The present results suggest that lattice vibrations are important for the occurrence of high temperature superconductivity.