Measurements Of Magnetic Penetration Depth Research Articles

In-Plane Magnetic Penetration Depth in Sr_{2}RuO_{4}: Muon-Spin Rotation and Relaxation Study.

We report on measurements of the in-plane magnetic penetration depth (λ_{ab}) in single crystals of Sr_{2}RuO_{4} down to ≃0.015 K by means of muon-spin rotation-relaxation. The linear temperature dependence of λ_{ab}^{-2} for T≲0.7 K suggests the presence of nodes in the superconducting gap. This statement is further substantiated by observation of the Volovik effect, i.e., the reduction of λ_{ab}^{-2} as a function of the applied magnetic field. The experimental zero-field and zero-temperature value of λ_{ab}=124(3) nm agrees with λ_{ab}≃130 nm, calculated based on results of electronic structure measurements reported in A. Tamai et al. [High-resolution photoemission on Sr_{2}RuO_{4} reveals correlation-enhanced effective spin-orbit coupling and dominantly local self-energies, Phys. Rev. X 9, 021048 (2019)PRXHAE2160-330810.1103/PhysRevX.9.021048]. Our analysis reveals that a simple nodal superconducting energy gap, described by the lowest possible harmonic of a gap function, does not capture the dependence of λ_{ab}^{-2} on T, so the higher angular harmonics of the energy gap function need to be introduced.

Generalization of interlayer tunneling models to cuprate superconductors with charge density waves

At the beginning of cuprate superconductors, the interlayer tunneling (ILT) and Lawrence-Doniach (L-D) models, which connect the CuO planes by Josephson coupling were considered the leading theoretical proposals for these materials. However, measurements of the interlayer magnetic penetration depth $\lambda_{c}$ yielded larger values than required by the ILT model. After the discovery of planar stripes and incommensurate charge ordering, it was also possible to consider Josephson coupling between these mesoscopic charge domains or blocks. We show that the average intralayer is larger than the interlayer coupling and comparable with the condensation energy, leading to a superconducting transition by long-range phase order. Another consequence is that the ratio $[\lambda_{c}/\lambda_{ab}]^2$ is directly proportional resistivity ratio $\rho_c/ \rho_{ab}$ near the superconducting transition temperature in agreement with several measurements.

Chiral superconductivity in UTe2 probed by anisotropic low-energy excitations

Chiral spin-triplet superconductivity is a topologically nontrivial pairing state with broken time-reversal symmetry, which can host Majorana quasiparticles. The heavy-fermion superconductor UTe2 exhibits peculiar properties of spin-triplet pairing, and the possible chiral state has been actively discussed. However, the symmetry and nodal structure of its order parameter in the bulk, which determine the Majorana surface states, remains controversial. Here we focus on the number and positions of superconducting gap nodes in the ground state of UTe2. Our magnetic penetration depth measurements for three field orientations in three crystals all show the power-law temperature dependence with exponents close to 2, which excludes single-component spin-triplet states. The anisotropy of low-energy quasiparticle excitations indicates multiple point nodes near the ky- and kz-axes in momentum space. These results can be consistently explained by a chiral B3u + iAu non-unitary state, providing fundamentals of the topological properties in UTe2.

Bulk evidence of anisotropic s-wave pairing with no sign change in the kagome superconductor CsV3Sb5

The recently discovered kagome superconductors AV3Sb5 (A = K, Rb, Cs) exhibit unusual charge-density-wave (CDW) orders with time-reversal and rotational symmetry breaking. One of the most crucial unresolved issues is identifying the symmetry of the superconductivity that develops inside the CDW phase. Theory predicts a variety of unconventional superconducting symmetries with sign-changing and chiral order parameters. Experimentally, however, superconducting phase information in AV3Sb5 is still lacking. Here we report the impurity effects in CsV3Sb5 using electron irradiation as a phase-sensitive probe of superconductivity. Our magnetic penetration depth measurements reveal that with increasing impurities, an anisotropic fully-gapped state changes to an isotropic full-gap state without passing through a nodal state. Furthermore, transport measurements under pressure show that the double superconducting dome in the pressure-temperature phase diagram survives against sufficient impurities. These results support that CsV3Sb5 is a non-chiral, anisotropic s-wave superconductor with no sign change both at ambient and under pressure.

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.

The FFLO State in the Dimer Mott Organic Superconductor κ-(BEDT-TTF)2Cu[N(CN)2]Br

The superconducting phase diagram for a quasi-two-dimensional organic superconductor, κ-(BEDT-TTF)2Cu[N(CN)2]Br, was studied using pulsed magnetic field penetration depth measurements under rotating magnetic fields. At low temperatures, Hc2 was abruptly suppressed even by small tilts of the applied fields owing to the orbital pair-breaking effect. In magnetic fields parallel to the conducting plane, the temperature dependence of the upper critical field Hc2 exhibited an upturn and exceeded the Pauli limit field HP in the lower temperature region. Further analyses with the second derivative of the penetration depth showed an anomaly at 31–32 T, which roughly corresponded to HP. The origin of the anomaly should not be related to the orbital effect, but the paramagnetic effect, which is almost isotropic in organic salts, because it barely depends on the field angle. Based on these results, the observed anomaly is most likely due to the transition between the Bardeen-Cooper-Schrieffer (BCS) and the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states. Additionally, we discuss the phase diagram and physical parameters of the transition by comparing them with other FFLO candidates.

Destruction of superconductivity through phase fluctuations in ultrathin a -MoGe films

We investigate the evolution of superconductivity with decreasing film thickness in ultrathin amorphous MoGe (a-MoGe) films using a combination of sub-Kelvin scanning tunneling spectroscopy, magnetic penetration depth measurements and magneto-transport measurements. We observe that superconductivity is strongly affected by quantum and classical phase fluctuations for thickness below 5 nm. The superfluid density is strongly suppressed by quantum phase fluctuations at low temperatures and evolves towards a linear-T dependence at higher temperatures. This is associated with a rapid decrease in the superconducting transition temperature, Tc, and the emergence of a pronounced pseudogap above Tc. These observations suggest that at strong disorder the destruction of superconductivity follows a Bosonic route where the global superconducting state is destroyed by phase fluctuations even though the pairing amplitude remains finite.

Measurement of magnetic penetration depth in superconducting films by two-coil mutual inductance technique

The magnetic penetration depth (<i>λ</i>) of a superconductor is an important parameter which connects the macroscopic electrodynamics with the microscopic mechanism of superconductivity. High-accuracy measurement of <i>λ</i> is of great significance for revealing the pairing mechanism of superconductivity and exploring the applications of superconductors. Among various methods used to measure <i>λ</i> of superconducting films, the two-coil mutual inductance (MI) technique has been widely adopted due to its high precision and simplicity. In this paper, we start with introducing the principle of MI technique and pointing out that its accuracy is mainly limited by the uncertainties in the geometric parameters (e.g. the distance between two coils) and the leakage flux around the film edge. On this basis, we build a homemade <i>transmission</i>-type MI device with a delicate design to achieve high-accuracy. Two coils are fixed by a single-crystal sapphire block machined with high precisions to minimize the uncertainty in geometry. As a result, the reproducibility in induced voltage measured with sample remounted is better than 4%. Besides, the flux leakage around the film edge is accurately determined by measuring a thick Nb film and Nb foils. The voltage induced by leakage flux is only around 1% of that measured in the normal state. Therefore, the absolute value of <i>λ</i> can be accurately extracted after flux leakage subtraction and normalization. It is shown that the error of the measured <i>λ</i> is less than 10% for a typical superconducting film with a thickness of 100 nm and a penetration depth of 150 nm. Furthermore, the performance of our apparatus is tested on epitaxial NbN films with thickness of 6.5 nm. The results show that the low temperature variation of superfluid density is well described by the dirty s-wave BCS theory, and at temperatures close to <i>T<sub>c</sub></i>, the superfluid density decrease drastically, owing to the Berezinski-Kosterlitz-Thouless transition transition. Moreover, the zero-temperature magnetic penetration depth and the superconducting energy gap extracted from the fitting parameters are both consistent with the reported values. Our device provides an ideal platform for carrying out detailed studies of the dependence of <i>λ</i> on temperature, chemical composition and epitaxial strain, etc. It could also be utilized to characterize other parameters of superconductor such as the critical current density, and when combined with the ionic liquid gating technique, our device offers an efficient route for revealing the microscopic mechanism of superconductivity.

Penetration depth study of the type-I superconductor PdTe2

Superconductivity in the topological non-trivial Dirac semimetal PdTe2 was recently shown to be type-I. We hereby report measurements of the relative magnetic penetration depth, , on several single crystals using a high precision tunnel diode oscillator technique. The temperature variation follows an exponential function for , consistent with a fully-gapped superconducting state and weak or moderately coupling superconductivity. By fitting the data we extract a -value of ∼500 nm. The normalized superfluid density is in good agreement with the computed curve for a type-I superconductor with nonlocal electrodynamics. Small steps are observed in , which possibly relates to a locally lower due to defects in the single crystalline sample.

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.

Strong antisymmetric spin–orbit coupling and superconducting properties: the case of noncentrosymmetric LaPtSi

In this work we aim to analyze the effect of a strong antisymmetric spin–orbit coupling (ASOC) on the superconductivity of noncentrosymmetric LaPtSi. We study the energy gap structure of polycrystalline LaPtSi by using magnetic penetration depth measurements down to 0.02Tc. We observed a dirty s-wave behavior, which provides compelling evidence that the spin-singlet component of the mixed pairing state is highly dominant. This is consistent with previous results in the sense that the mere presence of a strong ASOC does not lead to unconventional behaviors. Our result also downplays LaPtSi as a good candidate for realizing time-reversal invariant topological superconductivity.

High-precision measurement of magnetic penetration depth in superconducting films.

The magnetic penetration depth (λ) in thin superconducting films is usually measured by the mutual inductance technique. The accuracy of this method has been limited by uncertainties in the geometry of the solenoids and in the film position and thickness, by parasitic coupling between the coils, etc. Here, we present several improvements in the apparatus and the method. To ensure the precise thickness of the superconducting layer, we engineer the films at atomic level using atomic-layer-by-layer molecular beam epitaxy. In this way, we also eliminate secondary-phase precipitates, grain boundaries, and pinholes that are common with other deposition methods and that artificially increase the field transmission and thus the apparent λ. For better reproducibility, the thermal stability of our closed-cycle cryocooler used to control the temperature of the mutual inductance measurement has been significantly improved by inserting a custom-built thermal conductivity damper. Next, to minimize the uncertainties in the geometry, we fused a pair of small yet precisely wound coils into a single sapphire block machined to a high precision. The sample is spring-loaded to exactly the same position with respect to the solenoids. Altogether, we can measure the absolute value of λ with the accuracy better than ±1%.

Structural and Magnetic Phase Transitions near Optimal Superconductivity in BaFe2(As(1-x)Px)2.

We use nuclear magnetic resonance (NMR), high-resolution x-ray, and neutron scattering studies to study structural and magnetic phase transitions in phosphorus-doped BaFe2(As(1-x)P(x)2. Previous transport, NMR, specific heat, and magnetic penetration depth measurements have provided compelling evidence for the presence of a quantum critical point (QCP) near optimal superconductivity at x=0.3. However, we show that the tetragonal-to-orthorhombic structural (T{s}) and paramagnetic to antiferromagnetic (AF, TN) transitions in BaFe2(As(1-x)Px)2 are always coupled and approach T{N}≈T{s}≥T{c} (≈29 K) for x=0.29 before vanishing abruptly for x≥0.3. These results suggest that AF order in BaFe_{2}(As(1-x)Px)2 disappears in a weakly first-order fashion near optimal superconductivity, much like the electron-doped iron pnictides with an avoided QCP.

Superconducting and normal-state properties ofAPd2As2(A = Ca, Sr, Ba) single crystals

The synthesis and crystallography, magnetic susceptibility chi, magnetization M, specific heat Cp, in-plane electrical resistivity rho and in-plane magnetic penetration depth measurements are reported for single crystals of APd2As2 (A = Ca, Sr, Ba) versus temperature T and magnetic field H. The crystals were grown using PdAs self-flux. CaPd2As2 and SrPd2As2 crystallize in a collapsed body-centered tetragonal ThCr2Si2-type structure (I4/mmm), whereas BaPd2As2 crystallizes in the primitive tetragonal CeMg2Si2-type structure (P4/mmm), in agreement with literature data. The rho(T) data exhibit metallic behavior for all three compounds. Bulk superconductivity is reported for CaPd2As2 and SrPd2As2 below Tc = 1.27 and 0.92 K, respectively, whereas only a trace of superconductivity is found in BaPd2As2. No other phase transitions were observed. The chi(T) and M(H) data reveal anisotropic diamagnetism in the normal state, with chi_c > chi_ab for CaPd2As2 and BaPd2As2, and chi_c < chi_ab for SrPd2As2. The normal and superconducting state data indicate that CaPd2As2 and SrPd2As2 are conventional type-II nodeless s-wave electron-phonon superconductors. The electronic superconducting-state heat capacity data for CaPd2As2, which has an extremely sharp heat capacity jump at Tc, are analyzed using our recent elaboration of the alpha-model of the BCS theory of superconductivity, which indicates that the s-wave gap in this compound is anisotropic in momentum space.

Magnetic penetration depth and flux-flow resistivity measurements on NaFe0.97Co0.03As single crystals

We measured the surface impedance of NaFe1−xCoxAs (x≈0.03, optimally doped) single crystals under finite magnetic fields. At low temperatures (T<0.5Tc), the penetration depth of these crystals was increased as λ(T)−λ(0)=A×Tn with an exponent n≈2, indicating the realization of the gapless superconductivity. The flux-flow resistivity, ρf, behaved similarly to the Bardeen–Stephen prediction, ρf/ρn=B/Bc2. However, the electronic state inside the vortex core was not so dirty. By comparing the results with those of LiFeAs1−xPx and SrFe2(As0.7P0.3)2, it has been clarified that the gap anisotropy dominates the gradient of ρf(B).

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.

Nodal versus Nodeless Behaviors of the Order Parameters of LiFeP and LiFeAs Superconductors from Magnetic Penetration-Depth Measurements

High-precision measurements of magnetic penetration depth λ in clean single crystals of LiFeAs and LiFeP superconductors reveal contrasting behaviors. In LiFeAs the low-temperature λ(T) shows a flat dependence indicative of a fully gapped state, which is consistent with previous studies. In contrast, LiFeP exhibits a T-linear dependence of superfluid density infinity λ(-2), indicating a nodal superconducting order parameter. A systematic comparison of quasiparticle excitations in the 1111, 122, and 111 families of iron-pnictide superconductors implies that the nodal state is induced when the pnictogen height from the iron plane decreases below a threshold value of ~1.33 Å.

Superconducting energy gap in MgCNi3single crystals: Point-contact spectroscopy and specific-heat measurements

Specific heat has been measured down to 600 mK and up to 8 Tesla by the highly sensitive AC microcalorimetry on the MgCNi3 single crystals with Tc ~ 7 K. Exponential decay of the electronic specific heat at low temperatures proved that a superconducting energy gap is fully open on the whole Fermi surface, in agreement with our previous magnetic penetration depth measurements on the same crystals. The specific-heat data analysis shows consistently the strong coupling strength 2D/kTc ~ 4. This scenario is supported by the direct gap measurements via the point-contact spectroscopy. Moreover, the spectroscopy measurements show a decrease in the critical temperature at the sample surface accounting for the observed differences of the superfluid density deduced from the measurements by different techniques.

Measurement of magnetic penetration depth and superconducting energy gap in very thin epitaxial NbN films

We report the evolution of the magnetic penetration depth (λ) and superconducting energy gap (Δ) in epitaxial NbN films with thickness (d) varying between 51–3 nm. With decrease in film thickness Tc and Δ(0) monotonically decreases, whereas λ(0) monotonically increases. Our results show that while the values of Δ(0) and λ(0) are well described by Bardeen–Cooper–Schrieffer theory, at elevated temperatures, films with d≤6.5 nm show sudden drop in superfluid density associated with the Kosterlitz–Thouless–Berezinski transition. We discuss the implication of these results on the time response of superconducting bolometers made out of ultrathin NbN films.

Superconducting Properties of ${\rm V}_{3}{\rm Si}$ Thin Films Grown by Pulsed Laser Ablation

We present a systematic study of the superconducting properties of high quality V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Si thin films, grown by high vacuum pulsed laser deposition from a stoichiometric target, a technique never reported in literature for this compound. By changing both the substrate (crystal structure and orientation) and the deposition conditions (substrate temperature, target-substrate distance, laser frequency and pulse energy) the critical temperature and the resistivity values of the samples have been finely tuned. Best results (T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</sub> = 16.1 K and Residual Resistivity Ratio RRR = 8.5) are obtained for deposition temperatures higher than 1200degC on both LaAlO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> and MgO substrates. All the samples are polycrystalline, that however does not affect the good quality of the transport properties. The possibility of multiband superconductivity in this compound is investigated, probing as a function of temperature: (i) the critical field up to 28 T using voltamperometric measurements, and (ii) the superfluid density via magnetic penetration depth measurements with a single coil inductive technique operating in the MHz region.