Magnetic Penetration Depth Research Articles

Effect of low-temperature thermal annealing on the vortex dynamics of metastable β-Bi2Pd single crystals

We study the vortex dynamics on β-Bi2Pd single crystals with a superconducting critical temperature of 5.1 K. The upper critical fields and magnetic penetration depth are determined from magnetization measurements. At low temperatures, the self-field critical current density (Jc) is ≈ 20 kA/cm2. The vortex pinning energy, extracted from an Anderson-Kim approximation, is between 340 K and 140 K for fields between 100 G and 600 G. Differential scanning calorimetric measurements show that the crystals start to transform into the alpha-phase at temperatures as low as 60 °C. Short annealing at 100 °C modifies the pinning landscape increasing Jc mainly at temperatures below 3 K. The angular dependence of Jc from electrical transport experiments shows a broad peak when the magnetic field is parallel to the crystallographic c-axis, indicating the presence of correlated disorder.

Nodeless superconductivity in noncentrosymmetric LaRhSn

The superconducting order parameter of the noncentrosymmetric superconductor LaRhSn is investigated by means of low-temperature measurements of the specific heat, muon-spin relaxation/rotation $(\ensuremath{\mu}\mathrm{SR})$, and the tunnel-diode oscillator (TDO)-based method. The specific heat and magnetic penetration depth $[\ensuremath{\lambda}(T)]$ show an exponentially activated temperature dependence, demonstrating fully gapped superconductivity in LaRhSn. The temperature dependences of ${\ensuremath{\lambda}}^{\ensuremath{-}2}(T)$ deduced from the TDO-based method and $\ensuremath{\mu}\mathrm{SR}$ show nearly identical behavior, which can be well described by a single-gap $s$-wave model, with a zero-temperature gap value of $\mathrm{\ensuremath{\Delta}}(0)=1.77(4){k}_{B}{T}_{c}$. The zero-field $\ensuremath{\mu}\mathrm{SR}$ spectra do not show detectable changes upon cooling below ${T}_{c}$, and therefore there is no evidence for time-reversal-symmetry breaking in the superconducting state.

Microscopic evidence for anisotropic multigap superconductivity in the CsV3Sb5 kagome superconductor

The recently discovered kagome superconductor CsV3Sb5 (Tc ≃ 2.5 K) has been found to host charge order as well as a non-trivial band topology, encompassing multiple Dirac points and probable surface states. Such a complex and phenomenologically rich system is, therefore, an ideal playground for observing unusual electronic phases. Here, we report anisotropic superconducting properties of CsV3Sb5 by means of transverse-field muon spin rotation (μSR) experiments. The fits of temperature dependences of in-plane and out-of-plane components of the magnetic penetration depth suggest that the superconducting order parameter may have a two-gap (s + s)-wave symmetry. The multiband nature of superconductivity could be further supported by the different temperature dependences of the anisotropic magnetic penetration depth γλ(T) and upper critical field {gamma }_{{{{{rm{B}}}}}_{{{{rm{c}}}}2}}(T). The relaxation rates obtained from zero field μSR experiments do not show noticeable change across the superconducting transition, indicating that superconductivity does not break time reversal symmetry.

Evidence that cuprate superconductors form an array of nanoscopic Josephson junctions

Recent measurements of charge instabilities in overdoped compounds rekindled the proposal that cuprates become superconductors by long-range order through Josephson coupling between nanoscopic charge domains. We use the theory of phase-ordering dynamics to show that incommensurate charge density waves (CDWs) are formed in the CuO planes by a series of free-energy wells separated by steep barriers. Charge oscillations in these domains give rise to a net hole-hole attraction proportional to the height of these barriers. Concomitantly, the self-consistent calculations yield localized superconducting amplitudes in the CDW domains characterizing a granular superconductor. We show that a transition by long-range phase order promoted by Josephson coupling elucidates many well-known features of cuprates like the high magnetic penetration depth anisotropy and the origin of the pseudogap, among others. Furthermore, the average Josephson energy reproduces closely the planar superfluid density temperature dependence of La-based films and the superconducting giant proximity effects of cuprates, a 20-year-old open problem.

Nonreciprocal Meissner response in parity-mixed superconductors

Parity breaking gives rise to rich superconducting properties through the admixture of even- and odd-parity Cooper pairs. New light has been shed on parity-breaking superconductors by recent observations of nonreciprocal responses such as nonlinear optical responses and the superconducting diode effect. In this Letter, we demonstrate that nonreciprocal responses are characterized by a unidirectional correction to the superfluid density, which we call nonreciprocal superfluid density. This correction leads to the nonreciprocal Meissner effect, namely, the asymmetric screening of magnetic fields due to the nonreciprocal magnetic penetration depth. Performing a microscopic analysis of an exotic superconductor ${\mathrm{UTe}}_{2}$ and examining the temperature dependence and renormalization effect, we show that the nonreciprocal Meissner effect is useful to probe parity-mixing properties and gap structures in superconductors.

Role of Y substitution for Ca-site on magneto-resistivity properties of Bi-2212 superconductor rods prepared by LFZ

This comprehensive study delves into the effect of partial Y3+ substitution for Ca2+ in Bi2Sr2CaCu2O8+y superconducting rods prepared by the laser floating zone method (LFZ). The critical transition temperatures (Tconset, Tc, Tcoffset), activation energy (U), irreversibility field (Hirr), upper critical magnetic field (Hc2), coherence length (ξ), and penetration depth (λ) are determined by means of magneto-resistivity measurements performed between 0 and 5 T. According to the resistivity-temperature graph for zero fields, Tcoffset values tend to decrease regularly from 90.8 K to 87.1 K, and the residual resistivity values increase steadily from 0.14 to 9.7 mΩ .cm with the Y-content. The change of these two parameters is a sign that Y-introduction into the Bi-2212 matrix undermines the inter-grain coupling and increases the level of permanent-defects in the crystalline structure. However, the relatively high Tcoffset values and extremely low residual resistivity, especially in the pure and low Y-substituted samples, reflect the success of the LFZ process in growing homogeneous and well-oriented Bi-2212 grains. The resistivity transition broadening is observed when the applied field increases and Tcoffset values decrease dramatically, i.e. from 90.8 K to 72.1 K for the pure sample and from 87.1 K to 48.2 K for the 0.20Y-substituted ones. The calculated U values using the TAFF model decrease with the increase of the Y-content and the magnetic field. In addition, the magnetic field and temperature dependence of U is expressed by using U(H,T) ∼ ΔT H−η equation. Deduced parameters of Hirr and Hc2 from magneto-resistivity curves and theoretical findings of ξ and λ also favor the degradation of U values with the augmentation of Y-content in the Bi-2212 rods.

Observation of the non-linear Meissner effect

A long-standing theoretical prediction is that in clean, nodal unconventional superconductors the magnetic penetration depth λ, at zero temperature, varies linearly with magnetic field. This non-linear Meissner effect is an equally important manifestation of the nodal state as the well studied linear-in-T dependence of λ, but has never been convincingly experimentally observed. Here we present measurements of the nodal superconductors CeCoIn5 and LaFePO which clearly show this non-linear Meissner effect. We further show how the effect of a small dc magnetic field on λ(T) can be used to distinguish gap nodes from non-nodal deep gap minima. Our measurements of KFe2As2 suggest that this material has such a non-nodal state.

Holographic Abrikosov lattice: Vortex matter from black hole

The $\mathrm{AdS}/\mathrm{CFT}$ correspondence provides a unique way to study the vortex matter phases in superconductors. We solve the dynamical evolution of a superconductor in $2+1$ dimensions at a finite temperature subjected to a magnetic field quench in terms of a gravitational ``hairy black hole'' dual living in an asymptotic ${\mathrm{AdS}}_{4}$ space. We exploit this to determine the nature of the equilibrium states realized at long times after the quench of this two dimensional type II superconductor in a perpendicular external uniform magnetic field ${B}_{0}$. This holographic superconductor exhibits the generic lower (${B}_{c1}(T)$) and upper (${B}_{c2}(T)$) critical fields. For ${B}_{0}<{B}_{c1}(T)$ the magnetic field is completely expelled revealing the Meissner phase, while the superconductivity is destroyed when ${B}_{0}>{B}_{c2}(T)$. Abrikosov lattices appear in the range ${B}_{c1}(T)<{B}_{0}<{B}_{c2}(T)$ that realize various configurations in the form of hexagonal, square and slightly irregular square lattices pending the magnetic field strength and the influence of finite size boundaries. We show this to be consistent with the expectations of Ginzburg-Landau theory where the upper and lower critical fields are associated with the inverse squares of the coherence length and magnetic penetration depth, respectively.

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.

Magnetic Penetration Depth and Coherence Length in a Single‐Crystal YBa2Cu3O7−δ

Herein, DC magnetization measurements of high‐quality single crystals of optimally doped YBa2Cu3O7−δ(YBCO) superconductor are reported on. The temperature and orientation dependence of the magnetic penetration depth for single‐crystal YBCO is estimated from the slope of the linear M(lnH) dependence in the London regime. The penetration depth is strongly anisotropic. Also, the electrical resistivity as a function of temperature in YBCO thin film deposited by laser ablation on the SrTiO3 substrate face is investigated around the superconducting transition region under various values of the magnetic field up to 14 T. In this work, based on the resistivity measurements, the upper critical magnetic field for both directions B∥c‐axis and B⊥c‐axis is determined with a DC weak transport current density by using 90% criteria of the normal‐state resistivity value. According to the relations and , the coherence length (0) and (0) is determined, where is the magnetic flux quantum. The anisotropy parameter is calculated and analyzed within the frame of Ginzburg–Landau theory. This result indicates that anisotropy is more evident in YBCO.

Electronic structure, electron-phonon coupling, and superconductivity in noncentrosymmetric ThCoC2 from ab initio calculations

Superconductors without inversion symmetry in their crystal structure are known to exhibit unconventional properties. Recently, based on the measured temperature dependence of the magnetic field penetration depth, superconductivity in noncentrosymmetric $\mathrm{ThCoC_2}$ was proposed to be a nodal $d$-wave and mediated by the spin fluctuations. Moreover, a non-BCS behavior of the temperature dependence of the electronic specific heat and the magnetic upper critical field were reported. In this work, the electronic structure, phonons and electron-phonon coupling are studied in $\mathrm{ThCoC_2}$ on the basis of \textit{ab initio} computations. The effect of the spin-orbit coupling on the electronic structure and electron-phonon interaction is analyzed, and a large splitting of the electronic band structure is found. The calculated electron-phonon coupling constant $\lambda = 0.59$ remains in decent agreement with the experimental estimates, suggesting that the electron-phonon interaction is strong enough to explain superconductivity with $T_c \simeq 2.5$~K. Nevertheless, we show that the conventional isotropic Eliashberg formalism is unable to describe the thermodynamic properties of the superconducting state, as calculated temperature dependence of the electronic specific heat and magnetic penetration depth deviate from experiments, which is likely driven by the strong spin-orbit coupling and inversion symmetry breaking. In addition, to shed more light on the pairing mechanism, we propose to measure the carbon isotope effect, as our calculations based on the electron-phonon coupling predict the observation of the isotope effect with an exponent $\alpha \simeq 0.15$.

Nodeless superconductivity in the kagome metal CsV3Sb5

The recently discovered kagome metal series AV3Sb5 (A=K, Rb, Cs) exhibits topologically nontrivial band structures, chiral charge order and superconductivity, presenting a unique platform for realizing exotic electronic states. The nature of the superconducting state and the corresponding pairing symmetry are key questions that demand experimental clarification. Here, using a technique based on the tunneling diode oscillator, the magnetic penetration depth Δλ(T) of CsV3Sb5 was measured down to 0.07 K. A clear exponential behavior in Δλ(T) with marked deviations from a T or T2 temperature dependence was observed at low temperatures, indicating an absence of nodal quasiparticles. Temperature dependence of the superfluid density and electronic specific heat can be described by two-gap s-wave superconductivity, consistent with the presence of multiple Fermi surfaces in CsV3Sb5. These results evidence nodeless superconductivity in CsV3Sb5 under ambient pressure, and constrain the allowed pairing symmetry.

Campbell penetration depth in low carrier density superconductor YPtBi

Magnetic penetration depth, $\lambda_{m}$, was measured as a function of temperature and magnetic field in single crystals of low carrier density superconductor YPtBi by using a tunnel-diode oscillator technique. Measurements in zero DC magnetic field yield London penetration depth, $\lambda_{L}\left(T\right)$, but in the applied field the signal includes the Campbell penetration depth, $\lambda_{C}\left(T\right)$, which is the characteristic length of the attenuation of small excitation field, $H_{ac}$, into the Abrikosov vortex lattice due to its elasticity. Whereas the magnetic field dependent $\lambda_C$ exhibit $\lambda_{C}\sim B^{p}$ with $p=1/2$ in most of the conventional and unconventional superconductors, we found that $p\approx 0.23\ll1/2$ in YPtBi due to rapid suppression of the pinning strength. From the measured $\lambda_{C}(T,H)$, the critical current density is $j_{c}\approx40\,\mathrm{A}/\mathrm{cm^{2}}$ at 75 mK. This is orders of magnitude lower than that of conventional superconductors of comparable $T_{c}$. Since the pinning centers (lattice defects) and vortex structure are not expected to be much different in YPtBi, this observation is direct evidence of the low density of the Cooper pairs because $j_{c}\propto n_s$.

Determining the absolute value of magnetic penetration depth in small-sized superconducting films

In the previous four decades, the two-coil mutual inductance (MI) technique has been widely employed in characterizing magnetic penetration depth, , of superconducting films. However, the conventional methods used to obtain are not applicable to small-sized films with common shapes, which limits the application of the MI technique in superconductivity research. Here, we first employed the fast wavelet collocation (FWC) method to a two-coil system and then proposed the possibility of directly obtaining the absolute of polygonal superconducting films with arbitrary sizes. To verify its accuracy and advantages, we extracted the values of square NbN films with different sizes using the FWC and conventional flux leakage subtraction (FLS) methods. Notably, the FLS method fails for a film, which is attributed to the significant current peak at the film edge. In contrast, the absolute extracted using the FWC method was independent of the film size. Finally, we established the applicability of the FWC method to large coil spacings, which may pave the way for integrating high-accuracy measurements with the ionic liquid gating technique.

Relationship between superconductivity and nematicity in FeSe1−xTex (x=0−0.5) films studied by complex conductivity measurements

We measured the complex conductivity, $\sigma$, of FeSe$_{1-x}$Te$_x$ ($x=0-0.5$) films in the superconducting state which show a drastic increase of the superconducting transition temperature, $T_\textrm{c}$, when the nematic order disappears. Since the magnetic penetration depth, $\lambda$ $(>$ 400 nm), of Fe(Se,Te) is longer than the typical thickness of the film ($\sim$100 nm), we combined the coplanar waveguide resonator and cavity perturbation techniques to evaluate both the real and imaginary parts of $\sigma$. Films with a nematic order showed a qualitatively different temperature dependence in penetration depth and quasiparticle scattering time when compared with those without nematic order, suggesting that nematic order influences the superconducting gap structure. Conversely, the proportionality between superfluid density, $n_\textrm{s}$ ($\propto\lambda^{-2}$), and $T_\textrm{c}$ was observed irrespective of the presence or absence of nematic order. This result indicates that the amount of superfluid has a stronger impact on the $T_\textrm{c}$ of Fe(Se,Te) than the presence or absence of nematic order. Combining these results with band dispersions calculated using density functional theory, we propose that the change of the Fermi surface associated with nematicity is the primary factor influencing the change of $T_\textrm{c}$ and the superconducting gap structure in Fe(Se,Te).

Enhancing the effective critical current density in a Nb superconducting thin film by cooling in an inhomogeneous magnetic field

Quantitative magneto-optical imaging of a type-II superconductor thin film cooled under zero, homogeneous, and inhomogeneous applied magnetic fields indicates that the latter procedure leads to an enhancement of the screening capacity. Such an observation is corroborated by both B-independent and B-dependent critical state model analyses. Furthermore, repulsive (attractive) vortex–(anti)vortex interactions were found to have a decisive role in the shielding ability, with initial states prepared with vortices resulting in a shorter magnetic flux front penetration depth than those prepared with antivortices. The proposed strategy could be implemented to boost the performance of thin superconducting devices.

Complex conductivity of FeSe1–x Te x (x = 0 – 0.5) films

We measured the complex conductivity, σ, of the FeSe1−x Te x (x = 0 – 0.5) films below T c which show a drastic increase of the superconducting transition temperature, T c, when the nematic order disappears. Since the magnetic penetration depth, λ (> 400 nm) of Fe(Se, Te) is longer than the typical thickness of the film (∼100 nm), we combined the coplanar-waveguide-resonator- and cavity-perturbation techniques to evaluate both the real and imaginary parts of σ. Films with the nematic order showed a qualitatively different behavior of the quasiparticle scattering time compared with those without the nematic order, suggesting that the nematic order influences the superconducting gap structure. On the other hand, the proportionality between the superfluid density, n s/m* (∝ λ−2), and T c was observed irrespective of the presence or absence of the nematic order. This result indicates that the amount of the superfluid has a stronger impact on T c of Fe(Se, Te) than the presence or absence of the nematic order itself.

Large microwave inductance of granular boron-doped diamond superconducting films

Boron-doped diamond granular thin films are known to exhibit superconductivity with an optimal critical temperature of Tc=7.2 K. Here, we report the measured in-plane complex surface impedance of boron-doped diamond films in the microwave frequency range using a resonant technique. Experimentally measured inductance values are in good agreement with estimates obtained from the normal state sheet resistance of the material. The magnetic penetration depth temperature dependence is consistent with that of a fully gapped s-wave superconductor. Boron-doped diamond films should find application where high kinetic inductance is needed, such as microwave kinetic inductance detectors and quantum impedance devices.

Decisive proofs of the transition in the temperature dependence of the magnetic penetration depth

One of the features of the unconventional state in iron-based superconductors is possibility to transform to the s ++ state with the increase of the nonmagnetic disorder. Detection of such a transition would prove the existence of the state. Here we study the temperature dependence of the London magnetic penetration depth within the two-band model for the and s ++ superconductors. By solving Eliashberg equations accounting for the spin-fluctuation mediated pairing and nonmagnetic impurities in the T-matrix approximation, we have derived a set of specific signatures of the transition: (1) sharp change in the behavior of the penetration depth λ L as a function of the impurity scattering rate at low temperatures; (2) before the transition, the slope of increases as a function of temperature, and after the transition this value decreases; (3) the sharp jump in the inverse square of the penetration depth as a function of the impurity scattering rate, , at the transition; (4) change from the single-gap behavior in the vicinity of the transition to the two-gap behavior upon increase of the impurity scattering rate in the superfluid density ρ s (T).

Low kinetic inductance superconducting MgB2 nanowires with a 130 ps relaxation time for single-photon detection applications

Properties of superconducting nanowires set the performance level for superconducting nanowire single photon detectors (SNSPDs). Reset time in commonly employed large area SNSPDs, 1–10 ns, is known to be limited by the nanowire’s kinetic inductance to the load impedance ratio. On the other hand, reduction of the kinetic inductance in small area (waveguide integrated) SNSPDs prevents biasing them close to the critical current due to latching into a permanent resistive state. In order to reduce the reset time in SNSPDs, superconducting nanowires with both low kinetic inductance and fast electron energy relaxation are required. In this paper, we report on a study of kinetic inductance in narrow (15–100 nm) and long (up to 120 μm) superconducting MgB2 nanowires made from 5 nm thick films, offering such combination of properties. Such films were grown using hybrid physical chemical vapor deposition, resulting in a critical temperature of ∼32 K, and a switch current density of 5 × 107 A cm−2 (at 4.8 K). Using microwave reflectometry, we measured a kinetic inductance of L k0(4.8 K) = 1.3–1.6 pH/□ regardless of the nanowire width, which results in a magnetic field penetration depth of ∼90 nm. These values are very close to those in pristine MgB2. We showed that after excitations by a 50 fs pulsed laser the reset time in 35 nm × 120 μm MgB2 nanowires is 130 ps, which is more than a factor of 10 shorter than in NbN nanowires of similar length-to-width ratios. Depending on the bias current, such MgB2 nanowires function as single-, double, or triple-photon detectors for both visible (λ = 630 nm) and infrared (λ = 1550 nm) photons, with a dark count rate of <10 cps. Although the apparent photon detection efficiency seems so far to be low, further technological advances (uniform nanowire width, smaller thickness, increasing the switching current closer to the pair-breaking current) may improve this figure of merit.