Temperature Dependence Of Magnetic Penetration Depth Research Articles

Local spectroscopic evidence for a nodeless magnetic kagome superconductor CeRu2

We report muon spin rotation (µSR) experiments on the microscopic properties of superconductivity and magnetism in the kagome superconductor CeRu2 with K. From the measurements of the temperature-dependent magnetic penetration depth λ, the superconducting order parameter exhibits nodeless pairing, which fits best to an anisotropic s-wave gap symmetry. We further show that the /λ −2 ratio is comparable to that of unconventional superconductors. Furthermore, the powerful combination of zero-field (ZF)-µSR and high-field µSR has been used to uncover magnetic responses across three characteristic temperatures, identified as K, K, and K. Our experiments classify CeRu2 as an exceedingly rare nodeless magnetic kagome superconductor.

Isotropic s -wave superconductivity in the noncentrosymmetric charge density wave superconductor SrPt2As2

${\mathrm{SrPt}}_{2}{\mathrm{As}}_{2}$ undergoes a structural transition around 470 K (from a high-temperature tetragonal to a low-temperature orthorhombic phase) accompanied by a charge density wave transition and followed by a superconducting transition at much lower temperature (5 K). The superconducting gap symmetry of this noncentrosymmetric compound was investigated in detail by means of muon-spin rotation or relaxation $(\ensuremath{\mu}\mathrm{SR})$ experiments in transverse-field (TF) configuration. The temperature-dependent magnetic penetration depth obtained from the $\mathrm{TF}\text{\ensuremath{-}}\ensuremath{\mu}\mathrm{SR}$ spectra suggests an isotropic $s$-wave-type superconducting gap. No observable differences are seen in the asymmetry time spectra collected in zero field above and below the superconducting transition temperature ${T}_{c}$. This strongly suggests the absence of spontaneous magnetic fields in the superconducting state, hence pointing to a preserved time-reversal symmetry below ${T}_{c}$.

Superconducting order parameter of the nodal-line semimetal NaAlSi

Nodal-line semimetals are topologically nontrivial states of matter featuring band crossings along a closed curve, i.e., nodal-line, in momentum space. Through a detailed analysis of the electronic structure, we show, for the first time, that the normal state of the superconductor NaAlSi, with a critical temperature of Tc ≈ 7 K, is a nodal-line semimetal, where the complex nodal-line structure is protected by nonsymmorphic mirror crystal symmetries. We further report on muon spin rotation experiments revealing that the superconductivity in NaAlSi is truly of bulk nature, featuring a fully gapped Fermi-surface. The temperature-dependent magnetic penetration depth can be well described by a two-gap model consisting of two s-wave symmetric gaps with Δ1 = 0.6(2) meV and Δ2 = 1.39(1) meV. The zero-field muon experiment indicates that time-reversal symmetry is preserved in the superconducting state. Our observations suggest that, notwithstanding its topologically nontrivial band structure, NaAlSi may be suitably interpreted as a conventional London superconductor, while more exotic superconducting gap symmetries cannot be excluded. The intertwining of topological electronic states and superconductivity renders NaAlSi a prototypical platform to search for unprecedented topological quantum phases.

Evidence for unconventional superconductivity in half-Heusler YPdBi and TbPdBi compounds revealed by London penetration depth measurements

The half-Heusler compounds YPdBi and TbPdBi, while having similar band structure, exhibit different magnetic properties. YPdBi is a diamagnet, while TbPdBi shows antiferromagnetic order below 5.5 K. Both are superconductors with T${_c}\approx$1 K for YPdBi and T${_c}\approx$1.75 K for TbPdBi. Such a contrast in properties between these two compounds opens a question about the effects of band structure or magnetic correlations on superconductivity. Using the combination of a tunnel diode oscillator (TDO) and a commercial dilution refrigerator, we measured temperature dependent magnetic penetration depth $\Delta\lambda(T)$ in single crystals of YPdBi and TbPdBi, down to temperatures as low as 0.1K. We found that penetration depths of both compounds do not show exponential temperature dependence and saturation at low temperatures, as expected for conventional BCS superconductors. Instead, in both compounds, the penetration depth can be described by a power law $\Delta\lambda(T) = A\times T^{n}$. The coefficient A was found to be about 50$\%$ smaller in TbPdBi, but the exponents are very similar, $n = 2.76\pm 0.04$ in YPdBi and $n = 2.6\pm 0.3$ in TbPdBi, respectively. Our results suggest unconventional superconductivity in both YPdBi and TbPdBi.

Evidence for s -wave pairing with atomic scale disorder in the van der Waals superconductor NaSn2As2

The recent discovery of superconductivity in NaSn$_2$As$_2$ with a van der Waals layered structure raises immediate questions on its pairing mechanism and underlying electronic structure. Here, we present measurements of the temperature-dependent magnetic penetration depth $\lambda(T)$ in single crystals of NaSn$_2$As$_2$ down to $\sim40$ mK. We find a very long penetration depth $\lambda (0) = 960$ nm, which is strongly enhanced from the estimate of first-principles calculations. This enhancement comes from a short mean free path $\ell \approx 1.7$ nm, indicating atomic scale disorder possibly associated with the valence-skipping states of Sn. The temperature dependence of superfluid density is fully consistent with the conventional fully gapped s-wave state in the dirty limit. These results suggest that NaSn$_2$As$_2$ is an ideal material to study quantum phase fluctuations in strongly disordered superconductors with its controllable dimensionality.

Signatures of the topological s+\u2212 superconducting order parameter in the type-II Weyl semimetal Td-MoTe2

In its orthorhombic Td polymorph, MoTe2 is a type-II Weyl semimetal, where the Weyl fermions emerge at the boundary between electron and hole pockets. Non-saturating magnetoresistance and superconductivity were also observed in Td-MoTe2. Understanding the superconductivity in Td-MoTe2, which was proposed to be topologically non-trivial, is of eminent interest. Here, we report high-pressure muon-spin rotation experiments probing the temperature-dependent magnetic penetration depth in Td-MoTe2. A substantial increase of the superfluid density and a linear scaling with the superconducting critical temperature Tc is observed under pressure. Moreover, the superconducting order parameter in Td-MoTe2 is determined to have 2-gap s-wave symmetry. We also exclude time-reversal symmetry breaking in the superconducting state with zero-field μSR experiments. Considering the strong suppression of Tc in MoTe2 by disorder, we suggest that topologically non-trivial s+− state is more likely to be realized in MoTe2 than the topologically trivial s++ state.

Two-gap superconductivity inMo8Ga41and its evolution upon vanadium substitution

Zero-field and transverse-field muon spin rotation/relaxation ($\mu$SR) experiments were undertaken in order to elucidate microscopic properties of a strongly-coupled superconductor Mo$_{8}$Ga$_{41}$ with $T_{\text{c}}=9.8$ K. The upper critical field extracted from the transverse-field $\mu$SR data exhibits significant reduction with respect to the data from thermodynamic measurements indicating the coexistence of two independent length scales in the superconducting state. Accordingly, the temperature-dependent magnetic penetration depth of Mo$_{8}$Ga$_{41}$ is described using the model, in which two s-wave superconducting gaps are assumed. The V for Mo substitution in the parent compound leads to the complete suppression of one superconducting gap, and Mo$_{7}$VGa$_{41}$ is well described within the single s-wave gap scenario. The reduction in the superfluid density and the evolution of the low-temperature resistivity upon the V substitution indicate the emergence of a competing state in Mo$_{7}$VGa$_{41}$ that may be responsible for the closure of one of the superconducting gaps.

Full-Gap Superconductivity Robust against Disorder in Heavy-Fermion CeCu_{2}Si_{2}.

A key aspect of unconventional pairing by the antiferromagnetic spin-fluctuation mechanism is that the superconducting energy gap must have the opposite sign on different parts of the Fermi surface. Recent observations of non-nodal gap structure in the heavy-fermion superconductor CeCu_{2}Si_{2} were then very surprising, given that this material has long been considered a prototypical example of a superconductor where the Cooper pairing is magnetically mediated. Here we present a study of the effect of controlled point defects, introduced by electron irradiation, on the temperature-dependent magnetic penetration depth λ(T) in CeCu_{2}Si_{2}. We find that the fully gapped state is robust against disorder, demonstrating that low-energy bound states, expected for sign-changing gap structures, are not induced by nonmagnetic impurities. This provides bulk evidence for s_{++}-wave superconductivity without sign reversal.

Direct evidence for a pressure-induced nodal superconducting gap in the Ba0.65Rb0.35Fe2As2 superconductor.

The superconducting gap structure in iron-based high-temperature superconductors (Fe-HTSs) is non-universal. In contrast to other unconventional superconductors, in the Fe-HTSs both d-wave and extended s-wave pairing symmetries are close in energy. Probing the proximity between these very different superconducting states and identifying experimental parameters that can tune them is of central interest. Here we report high-pressure muon spin rotation experiments on the temperature-dependent magnetic penetration depth in the optimally doped nodeless s-wave Fe-HTS Ba0.65Rb0.35Fe2As2. Upon pressure, a strong decrease of the penetration depth in the zero-temperature limit is observed, while the superconducting transition temperature remains nearly constant. More importantly, the low-temperature behaviour of the inverse-squared magnetic penetration depth, which is a direct measure of the superfluid density, changes qualitatively from an exponential saturation at zero pressure to a linear-in-temperature behaviour at higher pressures, indicating that hydrostatic pressure promotes the appearance of nodes in the superconducting gap.

Magnetic penetration-depth measurements of a suppressed superfluid density of superconducting Ca0.5Na0.5Fe2As2single crystals by proton irradiation

We report on the dramatic effect of random point defects, produced by proton irradiation, on the superfluid density $\rho_{s}$ in superconducting Ca$_{0.5}$Na$_{0.5}$Fe$_2$As$_2$ single crystals. The magnitude of the suppression is inferred from measurements of the temperature-dependent magnetic penetration depth $\lambda(T)$ using magnetic force microscopy. Our findings indicate that a radiation dose of 2$\times10^{16}$cm$^{-2}$ produced by 3 MeV protons results in a reduction of the superconducting critical temperature $T_{c}$ by approximately 10%. % with no appreciable change in the slope of the upper critical fields. In contrast, $\rho_{s}(0)$ is suppressed by approximately 60%. This break-down of the Abrikosov-Gorkov theory may be explained by the so-called "Swiss cheese model", which accounts for the spatial suppression of the order parameter near point defects similar to holes in Swiss cheese. Both the slope of the upper critical field and the penetration depth $\lambda(T/T_{c})/\lambda(0)$ exhibit similar temperature dependences before and after irradiation. This may be due to a combination of the highly disordered nature of Ca$_{0.5}$Na$_{0.5}$Fe$_2$As$_2$ with large intraband and simultaneous interband scattering as well as the $s^\pm$-wave nature of short coherence length superconductivity.

Measurement of the magnetic penetration depth of a superconducting MgB2thin film with a large intraband diffusivity

We report the temperature-dependent magnetic penetration depth $\ensuremath{\lambda}(T)$ and the superconducting critical field ${H}_{c2}(T)$ in a 500-nm MgB${}_{2}$ film. Our analysis of the experimental results takes into account the two-gap nature of the superconducting state and indicates larger intraband diffusivity in the three-dimensional (3D) $\ensuremath{\pi}$ band compared to that in the two-dimensional (2D) $\ensuremath{\sigma}$ band. Direct comparison of our results with those reported previously for single crystals indicates that larger intraband scattering in the 3D $\ensuremath{\pi}$ band leads to an increase of $\ensuremath{\lambda}$. We calculated $\ensuremath{\lambda}$ and the thermodynamic critical field ${H}_{c}\ensuremath{\approx}2000$ Oe by employing the gap equations for two-band superconductors. Good agreement between the measured and calculated $\ensuremath{\lambda}$ value indicates the two independent measurements, such as magnetic force microscopy and transport, provide a venue for investigating superconducting properties in multiband superconductors.

Temperature dependent magnetic penetration depth of Co and Zn doped YBa 2Cu 3O 7 obtained from the AC susceptibility of magnetically aligned powders

We have measured the absolute value and temperature dependence of the magnetic penetration depth λ( T) of magnetically aligned cobalt and zinc doped YBa 2Cu 3O 7-δ (YBCO) using a commercial AC susceptometer. For pure YBCO, our values of λ ab (0)≅140 nm and λ c (0)≅1040 nm agree with other published values. We find increasing the Co doping increase both the fluctuation effects and the anisotropy ratio λ c /λ ab , probably due to the reduction of coupling in the c-direction, while doping with Zn substantially increases both λ ab and λ c . Our data imply a large, highly anisotropic gap whose maximum value is 2 Δ(0)≅10 k B T c. All samples show a T 2 term in both λ ab ( T) and λ c ( T) at low temperatures ( T<0.6 T c), in apparent disagreement with conventional s-wave BCS pairing. The possible explanations of this result are discussed.

Direct evidence for a very large penetration depth in superconducting Bi2Sr2CaCu2O8 single crystals

THE temperature-dependent magnetic penetration depth λ(T) and the superconducting coherence length ξ(T) are the two fundamental lengths in superconductivity1, and it is clearly important to determine these two quantities in the new high-transition-temperature (high-Tc) oxide superconductors2. Here we report a direct determination of λ(0) for high-quality single crystals of Bi2Sr2CaCu2O8 with a Tc of 85 K, for the particular case in which the screening currents responsible for the diamagnetism flow perpendicular to the CuO2 planes. The measured value, λc(0) = 100 ± 10 (μm, is surprisingly large, but it is consistent with the anisotropy in the electrical resistivity above Tc, measured on the same batch of single crystals, and approximately consistent with the anisotropy in lower critical field, Hc1 measured by others3. Such a large value may have important consequences for the physical properties of polycrystalline samples and thin films.