Penetration Depth Lambda Research Articles

Experimental signatures of nodeless multiband superconductivity in a hbox {2H-Pd}_{0.08} hbox {TaSe}_2 single crystal

In order to understand the superconducting gap nature of a hbox {2H-Pd}_{0.08} hbox {TaSe}_2 single crystal with T_{c} = 3.13 text { K}, in-plane thermal conductivity kappa , in-plane London penetration depth lambda _{text {L}}, and the upper critical fields H_{c2} have been investigated. At zero magnetic field, it is found that no residual linear term kappa _{0}/T exists and lambda _{text {L}} follows a power-law T^n (T: temperature) with n = 2.66 at T le frac{1}{3}T_c, supporting nodeless superconductivity. Moreover, the magnetic-field dependence of kappa _{0}/T clearly shows a shoulder-like feature at a low field region. The temperature dependent H_{c2} curves for both in-plane and out-of-plane field directions exhibit clear upward curvatures near T_c, consistent with the shape predicted by the two-band theory and the anisotropy ratio between the H_{c2}(T) curves exhibits strong temperature-dependence. All these results coherently suggest that hbox {2H-Pd}_{0.08} hbox {TaSe}_2 is a nodeless, multiband superconductor.

Time-reversal invariant and fully gapped unconventional superconducting state in the bulk of the topological compound Nb0.25Bi2Se3

Recently, the niobium (Nb)-doped topological insulator Bi_2Se_3, in which the finite magnetic moments of the Nb atoms are intercalated in the van der Waals gap between the Bi_2Se_3 layers, has been shown to exhibit both superconductivity with T_c = 3 K and topological surface states. Here we report on muon spin rotation experiments probing the temperature-dependent of effective magnetic penetration depth Lambda_eff(T) in the layered topological superconductor candidate Nb_0.25Bi_2Se_3. The exponential temperature dependence of lambda_(eff)^(-2)(T) at low temperatures suggests a fully gapped superconducting state in the bulk with the superconducting transition temperature T_c = 2.9 K and the gap to T_c ratio 2Delta/k_BT_c = 3.95(19). We also revealed that the ratio T_c/lambda_(eff)^(-2) is comparable to those of unconventional superconductors, which hints at an unconventional pairing mechanism. Furthermore, time reversal symmetry breaking was excluded in the superconducting state with sensitive zero-field muSR experiments. We hope the present results will stimulate theoretical investigations to obtain a microscopic understanding of the relation between superconductivity and the topologically non-trivial electronic structure of Nb_0.25Bi_2Se_3.

Study of in-plane electrical transport anisotropy of a -axis oriented YBa2Cu3O7−δ nanodevices

In the present work, we report the growth of fully untwinned high-quality a-axis-oriented YBa2Cu3O7-delta films on (100) SrLaGaO4 substrates by using PrBa2Cu3O7-delta as a buffer layer. We also fabricated nanowires at different angles gamma with respect to the [0,1,0] direction of the substrate and studied the in-plane anisotropy of the critical current density, which we explained by considering the anisotropy in the coherence length xi and London penetration depth lambda L. Finally, half-integer Shapiro-like steps measured in slightly underdoped c-axis oriented (gamma = 90 degrees) nanowires point towards a different transport regime, which could shed light on intriguing issues of high-critical-temperature superconductors.

Probing the pairing symmetry in the over-doped Fe-based superconductorBa0.35Rb0.65Fe2As2as a function of hydrostatic pressure

We report muon spin rotation experiments on the magnetic penetration depth lambda and the temperature dependence of lambda^{-2} in the over-doped Fe-based high-temperature superconductor (Fe-HTS) Ba_{1-x}Rb_ xFe_2As_2 (x = 0.65) studied at ambient and under hydrostatic pressures up to p = 2.3 GPa. We find that in this system lambda^{-2}(T) is best described by d-wave scenario. This is in contrast to the case of the optimally doped x = 0.35 system which is known to be a nodeless s^{+-}-wave superconductor. This suggests that the doping induces the change of the pairing symmetry from s^{+-} to d-wave in Ba_{1-x}Rb_{x}Fe_{2}As_{2}. In addition, we find that the d-wave order parameter is robust against pressure, suggesting that d is the common and dominant pairing symmetry in over-doped Ba_{1-x}Rb_{x}Fe_{2}As_{2}. Application of pressure of p = 2.3 GPa causes a decrease of lambda(0) by less than 5 %, while at optimal doping x = 0.35 a significant decrease of lambda(0) was reported. The superconducting transition temperature T_c as well as the gap to T_c ratio 2Delta/k_BT_c show only a modest decrease with pressure. By combining the present data with those previously obtained for optimally doped system x = 0.35 and for the end member x = 1 we conclude that the SC gap symmetry as well as the pressure effects on the SC quantities strongly depend on the Rb doping level. These results are discussed in the light of the putative Lifshitz transition, i.e., a disappearance of the electron pockets in the Fermi surface of Ba_{1-x}Rb_{x}Fe_{2}As_{2} upon hole doping.

Superconducting properties ofSn1−xInxTe(x=0.38–0.45)studied using muon-spin spectroscopy

The superconducting properties of Sn1-xInxTe (x = 0.38 to 0.45) have been studied using magnetization and muon-spin rotation or relaxation (muSR) measurements. These measurements show that the superconducting critical temperature Tc of Sn1-xInxTe increases with increasing x, reaching a maximum at around 4.8 K for x = 0.45. Zero-field muSR results indicate that time-reversal symmetry is preserved in this material. Transverse-field muon-spin rotation has been used to study the temperature dependence of the magnetic penetration depth lambda(T) in the mixed state. For all the compositions studied, lambda(T) can be well described using a single-gap s-wave BCS model. The magnetic penetration depth at zero temperature lambda(0) ranges from 500 to 580 nm. Both the superconducting gap Delta(0) at 0 K and the gap ratio Delta(0)/kBTc indicate that Sn1-xInxTe (x = 0.38 to 0.45) should be considered as a superconductor with intermediate to strong coupling.

Microwave Surface-Impedance Measurements of the Magnetic Penetration Depth in Single CrystalBa1−xKxFe2As2Superconductors: Evidence for a Disorder-Dependent Superfluid Density

We report high-sensitivity microwave measurements of the in-plane penetration depth lambda_{ab} and quasiparticle scattering rate 1/tau in several single crystals of the hole-doped Fe-based superconductor Ba(1-x)K(x)Fe(2)As(2) (x approximately 0.55). While a power-law temperature dependence of lambda_{ab} with a power approximately 2 is found in crystals with large 1/tau, we observe an exponential temperature dependence of the superfluid density consistent with the existence of fully opened two gaps in the cleanest crystal we studied. The difference may be a consequence of different levels of disorder inherent in the crystals. We also find a linear relation between the low-temperature scattering rate and the density of quasiparticles, which shows a clear contrast to the case of d-wave cuprate superconductors with nodes in the gap. These results demonstrate intrinsically nodeless order parameters in the Fe arsenides.

Two-Gap Superconductivity inBa1−xKxFe2As2: A Complementary Study of the Magnetic Penetration Depth by Muon-Spin Rotation and Angle-Resolved Photoemission

We investigate the magnetic penetration depth lambda in superconducting Ba1-xKxFe2As2 (Tc approximately 32 K) with muon-spin rotation (microSR) and angle-resolved photoemission (ARPES). Using microSR, we find the penetration-depth anisotropy gamma lambda=lambda c/lambda ab and the second-critical-field anisotropy gammaHc2 to show an opposite T evolution below Tc. This dichotomy resembles the situation in the two-gap superconductor MgB2. A two-gap scenario is also suggested by an inflection point in the in-plane penetration depth lambda ab around 7 K. The complementarity of microSR and ARPES allows us to pinpoint the values of the two gaps and to arrive to a remarkable agreement between the two techniques concerning the full T evolution of lambdaab. This provides further support for the described scenario and establishes ARPES as a tool to assess macroscopic properties of the superconducting condensate.

Evidence for a Nodal-Line Superconducting State in LaFePO

In several iron-arsenide superconductors there is strong evidence for a fully gapped superconducting state consistent with either a conventional s-wave symmetry or an unusual s{+/-} state where the gap changes sign between the electron and hole Fermi-surface sheets. Here we report measurements of the penetration depth lambda(T) in very clean samples of the related iron-phosphide superconductor, LaFePO, at temperatures down to approximately 100 mK. We find that lambda(T) varies approximately linearly with T strongly suggesting the presence of gap nodes in this compound. Taken together with other data, this suggests the gap function is not universal for all pnictide superconductors.

Unconventional London Penetration Depth in Single-CrystalBa(Fe0.93Co0.07)2As2Superconductors

The London penetration depth lambda(T) has been measured in single crystals of Ba(Fe0.93Co0.07)2As2. The observed low-temperature variation of lambda(T) follows a power law, Deltalambda(T) approximately T(n) with n approximately 2.4+/-0.1, indicating the existence of normal quasiparticles down to at least 0.02T(c). This is in contrast with previous penetration depth measurements on single crystals of NdFeAsO1-xFx and SmFeAsO1-xFx, which indicate an anisotropic but nodeless gap. We discuss possible explanations of the observed power law behavior.

Optical Study ofLaO0.9F0.1FeAs: Evidence for a Weakly Coupled Superconducting State

We have studied the reflectance of the recently discovered superconductor LaO0.9F0.1FeAs in a wide energy range from the far infrared to the visible regime. We report on the observation of infrared active phonons, the plasma edge, and possible interband transitions. On the basis of this data and the reported in-plane penetration depth lambda{L}(0)=254 nm [H. Luetkens, Phys. Rev. Lett. 101, 097009 (2008)] a disorder sensitive relatively small value of the total electron-boson coupling constant lambda{tot}=lambda{e-ph}+lambda{e-sp} approximately 0.6+/-0.35 can be estimated adopting an effective single-band picture.

Evidence for a Competition between the Superconducting State and the Pseudogap State of(BiPb)2(SrLa)2CuO6+δfrom Muon Spin Rotation Experiments

The in-plane magnetic penetration depth lambda ab in optimally doped (BiPb)2(SrLa)2CuO6+delta (OP Bi2201) was studied by means of muon-spin rotation. The measurements of lambda ab(-2)(T) are inconsistent with a simple model of a d-wave order parameter and a uniform quasiparticle weight around the Fermi surface. The data are well described assuming the angular gap symmetry obtained in ARPES experiments [Phys. Rev. Lett. 98, 267004 (2007)], which suggest that the superconducting gap in OP Bi2201 exists only in segments of the Fermi surface near the nodes. The remaining parts of the Fermi surface, which are strongly affected by the pseudogap state, do not contribute significantly to the superconducting condensate.

Coexistence of Magnetic Fluctuations and Superconductivity in the Pnictide High Temperature SuperconductorSmFeAsO1−xFxMeasured 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).

Muon-spin rotation measurements of the penetration depth of the Mo3Sb7 superconductor

Measurements of the magnetic-field penetration depth lambda in superconductor Mo3Sb7 (Tc~=2.1 K) were carried out by means of muon-spin rotation. The absolute values of lambda, the Ginzburg-Landau parameter kappa, and the first Hc1 and the second Hc2 critical fields at T=0 are lambda(0)=720(100) nm, kappa(0)=55(10), µ0Hc1(0)=1.8(3) mT, and µ0Hc2(0)=1.9(2) T. The zero-temperature value of the superconducting energy gap Delta(0) was found to be 0.35(1) meV, corresponding to the ratio 2Delta(0)/kBTc=3.83(10). At low temperatures lambda−2(T) saturates and becomes constant below T~=0.3Tc, in agreement with what is expected for s-wave BCS superconductors. Our results suggest that Mo3Sb7 is a superconductor with the single isotropic energy gap.

Multiple Gap Symmetries for the Order Parameter of Cuprate Superconductors from Penetration Depth Measurements

The temperature dependence of the London penetration depth lambda was measured for an untwinned single crystal of YBa_{2}Cu_{3}O_{7-delta} along the three principal crystallographic directions (a, b, and c). Both in-plane components (lambda_{a};{-2} and lambda_{b};{-2}) show an inflection point in their temperature dependence which is absent in the component along the c direction (lambda_{c};{-2}). The data provide convincing evidence that the in-plane superconducting order parameter is a mixture of (s+d)-wave symmetry whereas it is mainly s wave along the c direction. In conjunction with previous results it is concluded that coupled s+d-order parameters are universal and intrinsic to cuprate superconductors.

Observation of nonexponential magnetic penetration profiles in the Meissner state: A manifestation of nonlocal effects in superconductors

Implanting fully polarized low energy muons on the nanometer scale beneath the surface of a superconductor in the Meissner state enabled us to probe the evanescent magnetic field profile B(z)(0<z<=200nm measured from the surface). All the investigated samples [Nb: kappa \simeq 0.7(2), Pb: kappa \simeq 0.6(1), Ta: kappa \simeq 0.5(2)] show clear deviations from the simple exponential B(z) expected in the London limit, thus revealing the non-local response of these superconductors. From a quantitative analysis within the Pippard and BCS models the London penetration depth lambda_L is extracted. In the case of Pb also the clean limit coherence length xi0 is obtained. Furthermore we find that the temperature dependence of the magnetic penetration depth follows closely the two-fluid expectation 1/lambda^2 \propto 1-(T/T_c)^4. While B(z) for Nb and Pb are rather well described within the Pippard and BCS models, for Ta this is only true to a lesser degree. We attribute this discrepancy to the fact that the superfluid density is decreased by approaching the surface on a length scale xi0. This effect, which is not taken self-consistently into account in the mentioned models, should be more pronounced in the lowest kappa regime consistently with our findings.

Evidence for Line Nodes in the Superconducting Energy Gap of NoncentrosymmetricCePt3Sifrom Magnetic Penetration Depth Measurements

We report measurements of the magnetic penetration depth lambda(T) in high-quality CePt3Si samples down to 0.049 K. We observe a linear temperature dependence below T approximately equal to 0.16Tc, which is interpreted as evidence for line nodes in the energy gap of the low-temperature phase of this material. A kink in lambda(T) at about 0.53 K may be associated with the second superconducting transition recently reported. The results are discussed in terms of the symmetry of the superconducting order parameter.

Muon-Spin-Rotation Measurements of the Penetration Depth of the Infinite-Layer Electron-DopedSr0.9La0.1CuO2Cuprate 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.

Muon spin relaxation measurements of NaxCoO2.yH2O.

Using the transverse field muon spin relaxation technique, we measure the temperature dependence of the magnetic field penetration depth lambda, in the NaxCoO2.yH(2)O system. We find that lambda, which is determined by the superfluid density n(s) and the effective mass m*, is very small and on the edge of the TF-microSR sensitivity. Nevertheless, the results indicate that this system obeys the Uemura relation. By comparing lambda with the normal state electron density, we conclude that m* of the superconductivity carrier is 70 times larger than the mass of bare electrons. Finally, the order parameter in this system cannot be described by a complete gap over the entire Fermi surface.

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.

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.