Magnetic Penetration Depth Lambda Research Articles

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.

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.

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 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.

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 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.

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.

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.

Muon spin relaxation and isotropic pairing in superconducting PrOs4Sb12.

Transverse-field muon-spin rotation measurements in the vortex-lattice of the heavy-fermion (HF) superconductor PrOs4Sb12 yield a temperature dependence of the magnetic penetration depth lambda indicative of an isotropic or nearly isotropic energy gap. This is not seen to date in any other HF superconductor and is a signature of isotropic pairing symmetry, possibly related to a novel nonmagnetic "quadrupolar Kondo" HF mechanism in PrOs4Sb12. The T=0 relaxation rate sigma(s)(0)=0.91(1) micros(-1) yields an estimated magnetic penetration depth lambda(0)=3440(20) A, which is considerably shorter than in other HF superconductors.

Evidence for surface Andreev bound states in cuprate superconductors from penetration depth measurements.

Tunneling and theoretical studies have suggested that Andreev bound states form at certain surfaces of unconventional superconductors. Through studies of the temperature and field dependence of the in-plane magnetic penetration depth lambda(ab) at low temperature, we have found strong evidence for the presence of these states in clean single crystal YBCO and BSCCO. Crystals cut to expose (110) surfaces show a strong upturn in lambda(ab) at around 7 K, when the field is oriented along the c axis. In YBCO this upturn is completely suppressed by a field of approximately 0.1 T.

Magnetic penetration depth and critical current in YBaCuO thin films

The ab-plane magnetic penetration depth lambda in c-axis-oriented YBaCuO thin films was estimated from inductance measurements. The temperature dependence of lambda was shown to be consistent with the Bardeen-Cooper-Schrieffer (BCS) theory under the local limit condition. It was also shown that the experimentally obtained relationship among lambda (T=0), the resistivity p, and the critical temperature T/sub c/ was consistent with the theoretical one obtained from the local limit BCS theory. From that relationship, the value of lambda (T=0) could be deduced from p and T/sub c/. Moreover, the critical current was studied on the basis of the bias current dependence of lambda .< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Surface impedance measurements of YBa/sub 2/Cu/sub 3/O/sub 7/ thin films using coplanar resonators

The microwave response of linear and meander coplanar resonators fabricated from patterned thin films of YBa/sub 2/Cu/sub 3/O/sub 7/ (YBCO) on MgO substrates was studied. Unloaded quality factors in excess of 45000 at 2.36 GHz and 12 K were measured. From the calculated microwave current distribution in the resonator, upper limits of the intrinsic surface resistance of the best film at 15.9 GHz of 150 mu Omega and 690 mu Omega at 12 K and 77 K, respectively, were obtained. Values of the magnetic penetration depth lambda (0) in the films were estimated to be in the range 165-220 nm. It is possible to accurately fit 1/ lambda (T)/sup 2/ to the function 1-(T/T/sub c/)/sup 2/ over the whole of the available temperature range. This behavior is unlike that predicted by BCS theory, but it is probably extrinsic and can be explained by the enhanced field penetration at the film edges due to superconducting weak links. >

Measurement of the magnetic susceptibility of a rod-shaped superconductor using a solenoid coil (SRPM method)

An effective method for the measurement of the magnetic susceptibility ( chi ) of a circular rod-shaped superconductor, in which chi is estimated by substituting the magnetic penetration depth ( lambda ) into a formula after obtaining lambda from the difference in the impedance between a solenoid coil with a sample and an identical one without a sample, is proposed. The temperature dependence of chi obtained from this method has correlated well with the values measured with a SQUID magnetometer. >

Universal correlations between Tc and ns/m (carrier density over effective mass) in high-Tc cuprate superconductors.

The muon-spin-relaxation rate sigma has been measured in sixteen specimens of high-T/sub c/ cuprate superconductors (the 2:1:4, 1:2:3, 2:2:1:2, and 2:2:2:3 series). This has allowed us to study the magnetic field penetration depth lambda and thus the superconducting carrier density n/sub s/ divided by the effective mass m/sup */ (sigmaproportional1/lambda/sup 2/proportionaln/sub s//m/sup */). A universal linear relation between T/sub c/ and sigma(T..-->..0)proportionaln/sub s//m/sup */ has been found with increasing carrier doping. In heavily doped samples, however, T/sub c/ shows saturation and suppression with increasing n/sub s//m/sup */. This saturation starts at different values of n/sub s//m/sup */ for materials with different multiplicities of CuO planes.

Anisotropies in the magnetic penetration depth and critical current density of R/sub 1/Ba/sub 2/Cu/sub 3/O/sub 7-x/ (R=Y or Ho), measured on magnetically-aligned powder composites

Dispersed, uniaxially-aligned powder composites of R/sub 1/Ba/sub 2/Cu/sub 3/O/sub 7-x/ (R=Y or Ho) were formed by suspending the powder in a liquid organic matrix that was then solidified in a magnetic field. From the observed particle dimensions and magnetic susceptibility measurements for fields applied either parallel or perpendicular to the Cu-O planes, the authors infer anisotropies in the superconducting magnetic penetration depth lambda . From the magnetization hysteresis in the mixed state they derive relative anisotropies in the critical-current densities J/sub c/. The observed anisotropies are qualitatively similar for both rare-earth-based materials but show some quantitative distinctions.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Muon-spin-rotation measurement of magnetic field penetration and flux pinning in superconductingEuBa2Cu3Ox

Muon-spin-rotation measurements have been used to determine the magnetic field penetration depth lambda as a function of temperature T in superconducting, sintered EuBa/sub 2/Cu/sub 3/O/sub x/(xapprox. =7). The extrapolated value at 0 K, lambda(0), is 1700 A. The temperature dependence of lambda(T) in the interval 3.5 K to T/sub c/ is well described by the phenomenological relation lambda(T) = lambda(0)(1-(T/T/sub c/)/sup 4/)/sup -1/2/. For T