Penetration Depth λL Research Articles

Superconductivity of amorphous and crystalline Re–Lu films

We report on superconducting properties of a novel material: rhenium-lutetium films. Different compositions of Re x Lu binary are explored from x ≈ 3.8 to close to pure Re stoichiometry. The highest critical temperature, up to Tc≈ 7 K, is obtained for x ≈ 10.5 in accordance with electron dispersive spectroscopy results. Depending on the deposition conditions, polycrystalline or amorphous films are obtainable, both of which are interesting for practical use. Crystalline structure of polycrystalline phase is identified as a non-centrosymmetric superconductor using grazing incidence x-ray diffractometry. Superconducting properties were characterized both resistively and magnetically. Magnetoresistivity and AC/DC susceptibility measurements allowed us to determine Hc1 and Hc2 of these films, as well as estimate coherence length ξ(0) and magnetic penetration depth λL(0) . We also provide information on surface morphology of these films. Demonstration of superconductivity in this material justifies the point of view that Lu plays a role of group 3 transition metal in period 6 of the Periodic table of elements. Then, in analogy with Re–Nb, Re–Ti, Re–Hf and Re–Zr, one can expect that crystalline Re–Lu also breaks time-reversal symmetry. If that is proven by future experiments, in combination with noncentrosymmetric feature, these films could be used for forming nonreciprocal current devices, such as superconducting diodes, without involvement of external magnetic fields.

The Depairing Current Density of a Fe(Se,Te) Crystal Evaluated in Presence of Demagnetizing Factors

The effect of the demagnetizing factor, regarding the determination of the de-pairing current density Jdep, has been studied in the case of a Fe(Se,Te) crystal, using DC magnetic measurements as a function of a magnetic field (H) at different temperatures (T). First, the lower critical field Hc1(T) values were obtained, and the demagnetization effects acting on them were investigated after calculating the demagnetizing factor. The temperature behaviors of both the original Hc1 values and the ones obtained after considering the demagnetization effects (Hc1demag) were analyzed, and the temperature dependence of the London penetration depth λL(T) was obtained in both cases. In particular, the λL(T) curves were fitted with a power law dependence, indicating the presence of low-energy quasiparticle excitations. Furthermore, by plotting λL−2 as a function of T, we found that our sample behaves as a multigap superconductor, which is similar to other Fe-11 family iron-based compounds. After that, the coherence length ξ values were extracted, starting with the Hc2(T) curve. The knowledge of λL and ξ allowed us to determine the Jdep values and to observe how they are influenced by the demagnetizing factor.

The effect of the spin–orbit coupling on the physical properties of ScGa[formula omitted] and LuGa[formula omitted] superconductors

In this work, we have aimed to reveal the impacts of spin–orbit coupling (SOC) on the elastic, mechanical, electronic, phonon, and electron–phonon interaction properties of ScGa3 and LuGa3 by executing both scalar and full-relativistic ab initio pseudopotential calculations based on the density functional theory with its local density approximation. The effect of this coupling on the physical properties of LuGa3 is slightly more pronounced than those of ScGa3. This finding has a physical explanation because spin–orbit interaction in an atom is due to the interaction of electronic spin moment with the magnetic field formed by the traveling electron in the electric field of the nucleus. Since the nuclear charge enhances with the rise in atomic number of the elements, heavier atoms are characterized by larger SOC strength and the mass of Lu atom is considerably heavier than that of Sc atom. In particular, the inclusion of SOC changes the value of the electron–phonon coupling parameter for LuGa3 from 0.593 to 0.583 by less 2%, while the corresponding parameter of ScGa3 remains almost unchanged (from 0.536 to 0.537). The superconducting transition temperature is estimated to be 2.09 K for ScGa3, and 2.15 K for LuGa3 are almost equal to their experimental values of 2.1 and 2.2 K, respectively. Finally, we have estimated three superconducting parameters: the Ginzburg–Landau parameter (κ(0)), the London penetration depth (λL(0)) and the coherence length (ξ(0)). Their calculated values confirm the existence of type-I superconductivity in both superconductors.

Two distinctive temperature dependences of the London penetration depth in high-Tc cuprate superconductors as support for the theory of Bose-liquid superconductivity

In the framework of the theory of Bose-liquid superconductivity, we show that in high-Tc cuprate superconductors the magnetic field penetration depth (known as the London penetration depth λL(T)) decreases first exponentially below the superconducting transition temperature Tc with decreasing the temperature T and then λL(T) decreases like a certain power of T at lower temperatures due to the vanishing of the energy gap Δg(T) in the excitation spectrum of a superfluid Bose-liquid at a characteristic temperature Tc⁎ lower than Tc. Below Tc, the London penetration depth λL(T) has an exponential temperature dependence down to Tc⁎, which is different from a BCS- like exponential temperature dependence, and then λL(T) will follow a power law temperature dependence down to T=0, which is also different from power-law temperature dependences predicted by some BCS-like (d-wave) pairing theories. In unconventional (bosonic) cuprate superconductors characterized by the strong interboson coupling constant (γB≳1), λL(T) exhibits the distinctly different temperature dependences in different temperature intervals 0≤T≤Tc⁎<<Tc and Tc⁎<T<Tc when the energy gap Δg(T) vanishes at a temperature Tc⁎ well below Tc. In the weak interboson coupling (γB<<1) the energy gap Δg(T) vanishes at a temperature Tc⁎ close to Tc and the reduced London penetration depth λL(T)/λL(0) has an unusual Tn power-law temperature dependence in a wide temperature range 0<T<Tc⁎ below Tc, i.e. the expression λL(T)/λL(0)≃[1−aL(T)(T/Tc)n]−1/2 (where n≳4 and aL(T)≲1) is valid only below Tc⁎ and is similar to the well-known empirical Gorter-Casimir law. Our theoretical predictions of the distinctive power-law and exponential temperature dependences of λL(T)/λL(0) are in good agreement with the experimental results reported for GdBa2Cu3O7−δ ceramics and YBa2Cu3O7−δ films. The peculiar temperature dependences of λL(T)/λL(0) observed in these high-Tc materials at low and high temperatures do not follow the predictions of the s- and d-wave BCS-like theories of Fermi-liquid superconductivity and give evidence for the predictions of the theory of Bose-liquid superconductivity.

Superconducting boron doped nanocrystalline diamond microwave coplanar resonator

A coplanar waveguide resonator (CPR) is presented for kinetic inductance (Lk) and penetration depth (λL) measurements of superconducting boron doped nanocrystalline diamond (B-NCD) at microwave frequencies of 0.4 to 1.2 GHz and at temperatures below 3 K. Using finite element modelling and experimental measurements, this work demonstrates that thin granular B-NCD films (thickness d≈ 500nm) on Si have a large penetration depth (λL≈3.8μm), and therefore an associated high kinetic inductance per square (Lk,□≈ 670 to 690 pH/□). These values are much larger than those typically obtained for films on single crystal diamond, which is likely due to the high granularity of the nanocrystalline films. Based on the measured Q factors of the structure, the calculated surface resistance is found to be around ≈ 1 to 6μΩ at T<2 K in the 0.4 to 1.2 GHz range, demonstrating the potential for granular B-NCD for high quality factor superconducting microwave resonators and highly sensitive kinetic inductance detectors.

Superconducting gap structure in carrier doped BiCh2-based layered superconductors: A [formula omitted]SR study

The layered bismuth oxy-sulfide materials, which are structurally similar to Fe-pnictides/chalcogenides and cuprates superconductors, have sparked a lot of interest in the physics of reduced-dimensional superconductors. The pairing symmetry of the recently discovered BiCh2-based superconductor, La1−xCexOBiSSe with x = 0.3, was investigated using zero-field and transverse field (TF) muon spin measurements, as well as using magnetization and resistivity measurements. Resistivity and magnetization data confirmed bulk superconductivity below 2.7 K for x = 0.3. The temperature dependence of the magnetic penetration depth has been determined from TF-μSR data, which can be described by an isotropic two-gap s+s wave model compared to a single gap s- or anisotropic s-wave model, which resembles with Fe-pnictides/chalcogenides and MgB2. Furthermore, from the TF-μSR data, we have determined the London’s penetration depth λL(0) = 452(3) nm, superconducting carrier’s density ns = 2.18(1) × 1026 carriers/m3 and effective mass enhancement m∗ = 1.66(1) me, respectively. No signature of spontaneous internal field is found down to 100 mK in ZF-μSR measurement, which suggests that time-reversal symmetry is preserved in this system.

Magnetic field screening in hydrogen-rich high-temperature superconductors

In the last few years, the superconducting transition temperature, Tc, of hydrogen-rich compounds has increased dramatically, and is now approaching room temperature. However, the pressures at which these materials are stable exceed one million atmospheres and limit the number of available experimental studies. Superconductivity in hydrides has been primarily explored by electrical transport measurements, whereas magnetic properties, one of the most important characteristic of a superconductor, have not been satisfactory defined. Here, we develop SQUID magnetometry under extreme high-pressure conditions and report characteristic superconducting parameters for Im-3m-H3S and Fm-3m-LaH10—the representative members of two families of high-temperature superconducting hydrides. We determine a lower critical field Hc1 of ∼0.82 T and ∼0.55 T, and a London penetration depth λL of ∼20 nm and ∼30 nm in H3S and LaH10, respectively. The small values of λL indicate a high superfluid density in both hydrides. These compounds have the values of the Ginzburg-Landau parameter κ ∼12–20 and belong to the group of “moderate” type II superconductors, rather than being hard superconductors as would be intuitively expected from their high Tcs.

An Effective Model for Glueballs and Dual Superconductivity at Finite Temperature

The glueballs lead to gluon and QCD monopole condensations as by-products of color confinement. A color dielectric function G ∣ ϕ ∣ coupled with a Abelian gauge field is properly defined to mediate the glueball interactions at confining regime after spontaneous symmetry breaking (SSB) of the gauge symmetry. The particles are expected to form through the quark-gluon plasma (QGP) hadronization phase where the free quarks and gluons start clamping together to form hadrons. The QCD-like vacuum η 2 m η 2 F μ ν F μ ν , confining potential V c r , string tension σ , penetration depth λ , superconducting and normal monopole densities ( n s n n ), and the effective masses ( m η 2 and m A 2 ) will be investigated at finite temperature T . We also calculate the strong “running” coupling α s and subsequently the QCD β -function. The dual superconducting nature of the QCD vacuum will be investigated based on monopole condensation.

Twofold role of columnar defects in iron based superconductors

We report on the introduction of columnar defects in Ba1−xKxFe2As2 and BaFe2(As1−xPx)2 single crystals via 1.2 GeV Pb irradiation. Scanning transmission electron microscopy analysis proves the formation of continuous defects along the ion tracks, with a diameter of about 3 nm, and a planar density compatible with the irradiation fluence. The twofold role of such defects, i.e. as pair breakers as well as pinning centers, is investigated by a microwave technique, allowing us to determine critical temperature Tc, surface impedance and penetration depth λL, and by magneto-optical imaging and superconducting quantum interference device magnetometry to evaluate the critical current density Jc. The decrease of Tc is quite modest and, together with λL modifications, testifies the increase of pair-breaking scattering following irradiation. The dependence of Jc on irradiation dose and temperature is due to the pinning landscape induced by the columnar defects, and shows the existence of an optimal irradiation dose to enhance the critical current.

Determination of the Bardeen–Cooper–Schrieffer material parameters of the HIE-ISOLDE superconducting resonator

Superconducting material parameters of the Nb film coatings on the quarter-wave resonator for the HIE-ISOLDE project were studied by fitting experimental results with the Bardeen–Cooper–Schrieffer Mattis–Bardeen (BCS-MB) theory. We pointed out a strong correlation among fitted estimators of material parameters in the BCS-MB theory, and used a procedure to reduce the uncertainty by merging two χ2 distributions of the surface resistance and effective penetration depth. In this procedure, unlike previous studies, BCS coherence length (ξ0) and London penetration depth (λL) were not fixed at their literature values in the calculation because in our film, whose thickness is from 2 to 13 μm, they may take altered values as a consequence of microstructual defects. Since surface resistance and penetration depth have similar dependencies on coherence length and mean free path, the effects of the correlation between the estimators of these two parameters could not be mitigated by just combining surface resistance and penetration depth data. We used upper critical field measurement by SQUID magnetometry to provide a complementary constraint to these RF measurements, and this allowed all the material parameters to be obtained by fitting the experimental data. In the best performing cavity, the determined parameters are ξ0 = 29 nm, λL = 26 nm, mean free path l = 99 nm, and coupling strength Δ0/kBTc = 1.7. The coherence length is slightly shorter than for clean bulk Nb (39 nm) in the literature although the Nb film is thick and rather bulk-like. A poorly performing cavity showed weaker coupling constant Δ0/kBTc = 1.5 which may indicate film contamination during the coating process.

Structural, electro-magnetic, and optical properties of Ba(Fe,Ni)2As2 single-crystal thin film

We investigated the superconducting transition temperature (Tc), critical current density (Jc) and optical properties of optimally doped Ba(Fe0.95Ni0.05)2As2 (Ni-Ba122) single-crystalline epitaxial thin films grown by pulsed laser deposition for the first time. The Tc at zero resistivity was about 20.5 K and the Jc at self-field and 4.2 K was 2.8 MA cm−2 calculated by the Bean model. The superconducting properties such as Tc and Jc of thin films are comparable to those of bulk single-crystal samples. The superfluid plasma frequency (λp,S) of Ni-Ba122 thin film is ∼7033 cm−1 obtained by optical spectroscopic technique. Based on this plasma frequency, we obtained the London penetration depth (λL), ∼226 nm at 8 K, which is comparable to those of optimally Co- and K-doped BaFe2As2 single crystals.

All Superconducting Photonic Crystals with Wide-band Flat-top Responses in Visible Region

In this paper, transmission characteristics of one-dimensional all superconducting photonic crystals (SPCs) containing high and low temperature superconducting materials have been investigated in visible light region. For superconductor materials, both of the temperature dependence of refractive index and the amount of zero London penetration depth (λ L (0)) are important parameters. According to this, results indicate that by selecting proper superconductors and their thicknesses a wide-band flat-top transmission spectra for SPC structures is acquirable.

Superconductivity in the Th0.93Zr0.07B12 compound with UB12 prototype structure

In this work, we report superconductivity at 5.5 K in the new pseudo-ternary Th0.93Zr0.07B12 compound. We show clearly evidence that appropriate amounts of Zr substitution at the Th site induce the stabilization of the UB12 prototype structure at ambient pressure. The superconducting bulk properties of Th0.93Zr0.07B12 are confirmed by means of magnetization, electronic transport properties and specific heat measurements. The H–T phase diagrams based on magnetization and magnetoresistance measurements yield μ0Hc1(0)=6 mT and μ0Hc2(0)=98 mT and allow us to estimate the coherence length ξo∼57.9 nm and the penetration depth λL∼234 nm at zero kelvin.

Determination of the magnetic penetration depth in a superconducting Pb film

By means of scanning Hall probe microscopy technique, we accurately map the magnetic field pattern produced by Meissner screening currents in a thin superconducting Pb stripe. The obtained field profile allows us to quantitatively estimate the Pearl length Λ without the need of pre-calibrating the Hall sensor. This fact contrasts with the information acquired through the spatial field dependence of an individual flux quantum where the scanning height and the magnetic penetration depth combine in a single inseparable parameter. The derived London penetration depth λL coincides with the values previously reported for bulk Pb once the kinetic suppression of the order parameter is properly taken into account.

Strong Meissner screening change in superconducting radio frequency cavities due to mild baking

We investigate “hot” regions with anomalous high field dissipation in bulk niobium superconducting radio frequency cavities for particle accelerators by using low energy muon spin rotation (LE-μSR) on corresponding cavity cutouts. We demonstrate that superconducting properties at the hot region are well described by the non-local Pippard/BCS model for niobium in the clean limit with a London penetration depth λL=23±2 nm. In contrast, a cutout sample from the 120 ∘C baked cavity shows a much larger λ&amp;gt;100 nm and a depth dependent mean free path, likely due to gradient in vacancy concentration. We suggest that these vacancies can efficiently trap hydrogen and hence prevent the formation of hydrides responsible for rf losses in hot regions.

Elaboration of the α-model derived from the BCS theory of superconductivity

The single-band α-model of superconductivity (Padamsee et al 1973 J. Low Temp. Phys. 12 387) is a popular model that was adapted from the single-band Bardeen–Cooper–Schrieffer (BCS) theory of superconductivity mainly to allow fits to electronic heat capacity versus temperature T data that deviate from the BCS prediction. The model assumes that the normalized superconducting order parameter Δ(T)/Δ(0) and therefore the normalized London penetration depth λL(T)/λL(0) are the same as in BCS theory, calculated using the BCS value αBCS ≈ 1.764 of α ≡ Δ(0)/kBTc, where kB is Boltzmann’s constant and Tc is the superconducting transition temperature. On the other hand, to calculate the electronic free energy, entropy, heat capacity and thermodynamic critical field versus T, the α-model takes α to be an adjustable parameter. Here we write the BCS equations and limiting behaviors for the superconducting state thermodynamic properties explicitly in terms of α, as needed for calculations within the α-model, and present plots of the results versus T and α that are compared with the respective BCS predictions. Mechanisms such as gap anisotropy and strong coupling that can cause deviations of the thermodynamics from the BCS predictions, especially the heat capacity jump at Tc, are considered. Extensions of the α-model that have appeared in the literature, such as the two-band model, are also discussed. Tables of values of Δ(T)/Δ(0), the normalized London parameter Λ(T)/Λ(0) and λL(T)/λL(0) calculated from the BCS theory using α = αBCS are provided, which are the same in the α-model by assumption. Tables of values of the entropy, heat capacity and thermodynamic critical field versus T for seven values of α, including αBCS, are also presented.

Pinning and transport properties of undoped and Sn-dopedMoSr2YCu2O8 − δ

We investigated the pinning and transport properties of samples with nominal compositionsMoSnxSr2YCu2O8 − δ (x = 0 and 0.03) as a function of the temperature and magnetic field. It was establishedthat Mo-1212 is a highly anisotropic superconductor with the formationof 2D vortices. The Sn doping increases the anisotropy and modifies theintergrain superconductivity of Mo-1212. The temperature dependences of theresistivity of the undoped and Sn-doped Mo-1212 were described by the relationρ(T) = (ρ0/T)exp(−U/kBT). The fit to this relation indicates the temperature range of applicationof the flux-creep approximation. We determined the penetration depthλ, the coherencelength ξ and theattempt frequency ν0 of Mo-1212. The field dependences of the parametersρ0 andU denoted the presence of a crossover field. Some interpretations of the latter field, aswell as the nonlinear electric field versus current density characteristics, werediscussed.

Possible indicators for low dimensional superconductivity in the quasi-1D carbide Sc3CoC4

The transition metal carbide Sc3CoC4 consists of a quasi-one-dimensional (1D) structure with [CoC4]∞ polyanionic chains embedded in a scandium matrix. At ambient temperatures Sc3CoC4 displays metallic behavior. At lower temperatures, however, charge density wave formation has been observed around 143 K which is followed by a structural phase transition at 72 K. Below Tconset = 4.5 K the polycrystalline sample becomes superconductive. From Hc1(0) and Hc2(0) values we could estimate the London penetration depth (λL ≊ 9750 Å) and the Ginsburg-Landau (GL) coherence length (ξGL ≊ 187 Å). The resulting GL-parameter (κ ≊ 52) classifies Sc3CoC4 as a type II superconductor. Here we compare the puzzling superconducting features of Sc3CoC4, such as the unusual temperature dependence i) of the specific heat anomaly and ii) of the upper critical field Hc2(T) at Tc, and iii) the magnetic hysteresis curve, with various related low dimensional superconductors: e.g., the quasi-1D superconductor (SN)x or the 2D transition-metal dichalcogenides. Our results identify Sc3CoC4 as a new candidate for a quasi-1D superconductor.

Relationship between intrinsic surface resistance and critical current density of YBCO thin films with various thickness

We investigated the relationship between the intrinsic surface resistance (Rsint) and critical current density (Jc) of YBa2Cu3Oy (YBCO) film thinner than the penetration depth (λL). The measured YBCO films were deposited on CeO2-buffered r-cut Al2O3 substrates by the pulsed laser deposition method. The thicknesses of these films were 300, 200, and 100nm, respectively. The Rsint means the surface resistance of YBCO film removing the loss by the impedance of the substrates. The effective surface resistance (Rseff) including the impedance of the substrate and the Jc of each YBCO film were measured using the dielectric resonator method at 21.8GHz and the inductive method. We calculated Rsint by using phenomenological expressions and the Rseff value. The Rsint values of each YBCO film were almost the same in the measured temperature region. As a result, we found that Rsint was in inverse proportion to the Jc of YBCO film thinner than λL.

Investigation of Li-doped MgB2

We present a systematic characterization ofMg1−xLixB2 polycrystalline samples with nominal Li contentx up to 0.30. We explore the effectiveness of the substitution and investigate its influence onsuperconducting and normal state properties. The structural analyses by neutron and x-raydiffraction indicate that, despite the lattice parameters remaining unchanged within theexperimental accuracy, around 30% of the nominal Li content actually enters the structure.Also the transition temperature is only weakly affected by Li substitution, but its relationshipwith the residual resistivity and magnetoresistivity data is compatible with a picture whereπ bands are filled with holes and/or affected by disorder, as predictedby theory. We also measured the magnetic penetration depthλ by an inductance technique. Data fits based on the standardBardeen–Cooper–Schrieffer two-band model yield the zero-temperature limit of bothλ and superconductinggaps: we find that λ(0) increases weakly and quickly saturates with increasingx, whereasΔπ(0) andΔσ(0) decreasewith x. This analysis suggests that lithium substitution induces disorder mainly in theπ band. Point contact spectroscopy results on samples obtained from the same batch are infull agreement with magnetic penetration depth data on the undoped sample, but givesuperconducting gaps almost insensitive to Li substitution, showing at most a small increase inΔπ(0) that may be related to an inhomogeneous distribution of Li content.