Single crystal of Lu$_2$Fe$_3$Si$_5$ was studied with the tunnel-diode resonator technique in Meissner and mixed states. Temperature dependence of the superfluid density provides strong evidence for the two-gap superconductivity with almost equal contributions from each gap of magnitudes $Δ_1/k_BT_c=1.86$ and $Δ_1/k_BT_c=0.54$. In the vortex state, pinning strength shows unusually strong temperature dependence and is non-monotonic with the magnetic field (peak effect). The irreversibility line is sharply defined and is quite distant from the $H_{c2}(T)$, which hints on to enhanced vortex fluctuations in this two-gap system. Altogether our findings provide strong electromagnetic - measurements support to the two-gap superconductivity in Lu$_2$Fe$_3$Si$_5$ previously suggested from specific heat measurements.
We have measured the magnetic penetration depth of the recently discovered binary superconductor MgB_2 using muon spin rotation and low field $ac$-susceptibility. From the damping of the muon precession signal we find the penetration depth at zero temperature is about 85nm. The low temperature penetration depth shows a quadratic temperature dependence, indicating the presence of nodes in the superconducting energy gap.
The two-orbital superconducting state is modeled by on-site intra-orbital negative-U Hubbard correlations together with inter-orbital pair-transfer interactions. The critical temperature is mainly governed by intra-orbital attractive interactions and it can pass through an additional maximum as a function of band filling. For the certain number of electrons the clear interband proximity effect is observable in the superconducting state of the band with a smaller gap. The influence of band fillings and orbital site energies on the temperature dependencies of two-component superconductivity cohe…
The effective superconducting penetration depth measured in the vortex state of PrOs4Sb12 using transverse-field muon spin rotation (TF-muSR) exhibits an activated temperature dependence at low temperatures, consistent with a nonzero gap for quasiparticle excitations. In contrast, Meissner-state radiofrequency (rf) inductive measurements of the penetration depth yield a T^2 temperature dependence, suggestive of point nodes in the gap. A scenario based on the recent discovery of extreme two-band superconductivity in PrOs4Sb12 is proposed to resolve this difference. In this picture a large diffe…
Based on the third law of thermodynamics it is shown, that the first derivative of the magnetic penetration depth with respect to temperature should vanish irrespective of the symmetry of Cooper pairs.
We measured the magnetic penetration depth $λ(T)$ in single crystals of LaOs$_{4}$Sb$_{12}$ ($T_c$=0.74 K) down to 85 mK using a tunnel diode oscillator technique. The observed low-temperature exponential dependence indicates a s-wave gap. Fitting the low temperature data to BCS s-wave expression gives the zero temperature gap value $Δ(0)= (1.34 \pm 0.07) k_B T_c$ which is significantly smaller than the BCS value of 1.76$k_B T_c$. In addition, the normalized superfluid density $ρ(T)$ shows an unusually long suppression near $T_c$, and are best fit by a two-band s-wave model.
The London penetration depth plays a key role in determining and uncovering many properties of a superconductor, including homogeneity, anisotropy, isotope effects, importance of quantum and thermal fluctuations, and facets of the nature of superconductivity in a particular material. Guided by the generic phase diagram in the temperature-dopant concentration plane we examine experimental data on the temperature, isotope substitution, inhomogeneity and magnetic field dependence of the penetration depths to uncover some facets of the mystery of superconductivity in the cuprates
The London penetration depth, $λ(T)$, was measured in polycrystalline powders of the non-oxide perovskite superconductor $\mathrm{MgCNi_3}$ by using a sensitive tunnel-diode resonator technique. The penetration depth exhibits distinctly non s-wave BCS low-temperature behavior, instead showing quadratic temperature dependence, suggestive of a nodal order parameter.
We report measurements of the temperature dependence of the electrical resistivity, ρ(T), and magnetic penetration depth, λ(T), for polycrystalline samples of Eu_0.5K_0.5Fe_2As_2 with Tc=31 K. $ρ(T)$ follows a linear temperature dependence above T_c and bends over to a weaker temperature dependence around 150 K. The magnetic penetration depth, determined by radio frequency technique displays an unusual minimum around 4 K which is associated with short-range ordering of localized Eu3+ moments.
Transverse-field muon spin rotation ($μ$SR) experiments in the heavy-fermion superconductor PrOs$_{4}$Sb$_{12}$ ($T_{c}=1.85$ K) suggest that the superconducting penetration depth $λ(T)$ is temperature-independent at low temperatures, consistent with a gapped quasiparticle excitation spectrum. In contrast, radiofrequency (rf) inductive measurements yield a stronger temperature dependence of $λ(T)$, indicative of point nodes in the gap. This discrepancy appears to be related to the multiband structure of PrOs$_{4}$Sb$_{12}$. Muon Knight shift measurements in PrOs$_{4}$Sb$_{12}$ suggest that the…
A method is presented to measure the absolute value of the London penetration depth, $λ$, from the frequency shift of a resonator. The technique involves coating a high-$T_c$ superconductor (HTSC) with film of low - Tc material of known thickness and penetration depth. The method is applied to measure London penetration depth in YBa2Cu3O{7-δ} (YBCO) Bi2Sr2CaCu2O{8+δ} (BSCCO) and Pr{1.85}Ce{0.15}CuO{4-δ}$ (PCCO). For YBCO and BSCCO, the values of $λ(0)$ are in agreement with the literature values. For PCCO $λ\approx 2790$ Å, reported for the first time.
In- and out-of-plane London penetration depths were measured in single crystals CaAlSi (T_{c}=6.2 K and 7.3 K) using a tunnel-diode resonator. A full 3D BCS analysis of the superfluid density is consistent with a prolate spheroidal gap, with a weak-coupling BCS value in the ab-plane and stronger coupling along the c-axis. The gap anisotropy was found to significantly decrease for higher T_{c} samples.
We calculate the doping dependence of the penetration depths and optical sum rule violation in La_(2-x)Sr_xCuO_4 within the model of hole superconductivity. In the clean limit the predicted in-plane sum rule violation is larger than the c-axis one, however in the presence of disorder the latter one becomes very substantially enhanced.
We present an analysis of previously published measurements of the London penetration depth of layered organic superconductors. The predictions of the BCS theory of superconductivity are shown to disagree with the measured zero temperature, in plane, London penetration depth by up to two orders of magnitude. We find that fluctuations in the phase of the superconducting order parameter do not determine the superconducting critical temperature as the critical temperature predicted for a Kosterlitz--Thouless transition is more than an order of magnitude greater than is found experimentally for so…
We investigate the effect of anti-ferromagnetic (AF) quantum criticality on the magnetic penetration depth $λ(T)$ in line-nodal superconductors, including the cuprates, the iron pnictides, and the heavy-fermion superconductors. The critical magnetic fluctuation renormalizes the current vertex and drastically enhances zero-temperature penetration depth $λ(0)$, which is more remarkable in the iron-pnictide case due to the Fermi-surface topology. Additional temperature ($T$) dependence of the current renormalization makes the expected $T$-linear behavior at low temperatures approaching to $T^{1.5…
Application of a tunnel-diode resonator (TDR) technique for studies of the vortex response in magnetic superconductors is described. Operating at very small excitation fields and sufficiently high frequency, TDR was used to probe small-amplitude linear AC response in several types of single crystals where long-range magnetic order coexists with bulk superconductivity. Full local - moment ferromagnetism destroys superconductivity and can coexist with it only in a narrow temperature range ($\sim 0.3$ K). In contrast, weak ferromagnetic as well as antiferromagnetic orders can coexist with bulk su…
The penetration depth of FFLO d-wave superconductors is calculated, in presence of additional magnetic field for both parallel and perpendicular to the internal FFLO magnetic field, when the nonlocal effects are dominated. The generalized Gorkov equations have been used to obtain the linearized response kernel. It is shown that extra term added to total kernel with no spatially gap is proportional to the momentum of FFLO Cooper pairs, Q. For the case parallel to the internal FFLO magnetic field, below a crossover temperature T*, it is shown that Lambda(T)-Lambda(0) is proportional to T^3 for b…
We report measurements of the temperature dependence of the magnetic penetration depth λ(T) in non-centrosymmetric superconductor Re_3W. We employed two experimental techniques: extraction of λ(T) from magnetic {\em dc}-susceptibility, measured on a powder sample, and the rf tunnel diode resonator technique, where a bulk polycrystalline sample was used. The results of both techniques agree: the temperature dependence of the penetration depth can be well described by weak-coupling, dirty-limit, s-wave BCS theory where we obtain $Δ(0)/k_BT_C=1.76$. No evidence for unconventional pairing resultin…
Muon spin spectroscopy measurements have been used to study the superconducting state of FeTe0.5Se0.5. The temperature dependence of the in-plane magnetic penetration depth, lambda_ab(T), is found to be compatible with either a two gap s+s wave or an anisotropic s-wave model. The value for lambda_ab(T) at T=0 K is estimated to be lambda_ab(0)=534(2)nm.
The London penetration depth for the unconventional superconductor Sr$_2$RuO$_4$ is analyzed assuming an order parameter which breaks time reversal symmetry and parity simultaneously. Such a superconducting state possesses chiral quasiparticle states with subgap energies at the surface. We show that these subgap states can give a significant contribution to the low-temperature behavior of the London penetration depth yielding a $ T^2 $ power-law even though bulk quasiparticle spectrum is gapped. The presence of several electron bands gives rise to interband transition among the subgap surface …
The apparent $T^2$-temperature dependence of the London penetration depth in Sr$_2$RuO$_4$ is discussed on the basis of a multi-gap model with horizontal line nodes. The influence of the nodes in combination with nonlocal electromagnetic response leads to low-temperature behaviors as $-T^2\ln T$ in the London limit and as $T^2$ in the Pippard limit. These behaviors appear only at very low temperature. On the other hand, the interplay of the superconductivity of different bands is responsible for the observed $T^2$-like behavior over the wide temperature range. The experimental data can be fitt…
The ${}^{11}$B NMR spectra in polycrystalline MgB$_2$ were measured for several magnetic fields (1.97 T and 3.15 T) as a function of temperature from 5 K to 40 K. The composite spectra in the superconducting state can be understood in terms of anisotropy of the upper critical field, $γ_{H}$, which is determined to be 5.4 at low temperature. Using Brandt's algorithm\cite{Brandt} the full spectrum, including satellites, was simulated for the temperature 8 K and a magnetic field of 1.97 T. The penetration depth $λ$ was determined to be $1,152\pm50$ Å, and the anisotropy of the penetration depth, …
The temperature dependence of the in-plane, λ_{\parallel}, and interplane, λ_{\perp}, London penetration depth was measured in the metal-free all-organic superconductor β-ET (see title) ($T_c \approx$ 5.2 K). λ_{\parallel} ~T^3 up to 0.5 Tc, a power law previously observed only in materials thought to be p-wave superconductors. λ_{\perp} is larger than the sample dimensions down to the lowest temperatures (0.35 K), implying an anisotropy of λ_{\perp}/λ_{\parallel} ~ 400-800.
The London penetration depth $λ(T)$ has been measured in single crystals of Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ using the tunnel diode resonator technique. The measured doping levels of $x=$~0.038, 0.047, 0.058, 0.074 and 0.10 range from underdoped to overdoped concentrations. The measurements have shown that the density of carriers participating in superconductivity decreases sharply in the underdoped regime, but the penetration depth as a function of temperature exhibits a robust power law, $Δλ(T)\sim T^{n}$, for all measured dopings, with $n$ between 2 and 2.5. We discuss the implications …
We review and refine the finite size scaling analysis of specific heat and London penetration depths data of cuprate superconductors and compare it to the analysis of specific heat measurements near the superfluid transition of 4He confined to 1mum^3 cylindrical boxes. This system crosses from 3D to 0D behavior near the transition. This has a marked effect on the specific heat as seen by a pronounced rounding of the maximum and a shift to a temperature lower than the transition temperature of the bulk system. The region in between the 3D to 0D crossover uncovers the contributions from the surf…
We study the effect of Coulomb repulsion between oxygen holes on the London penetration depth $λ$ based on the concept of spin-polaron nature of Fermi quasiparticles in cuprates superconductors. It is shown that for the generally accepted values of the parameters of the spin-fermion model, taking into account the Coulomb interaction, both the one-site Hubbard $U_p$ and interaction between the holes on next-nearest-neighbor oxygen ions $V_2$, allows one to achieve a much better agreement of the calculated temperature dependencies of the value $λ^{-2}$ with the experimental data in La$_{2-x}$Sr$…
In the tetragonal heavy fermion system CeCoIn5 the unconventional superconducting state is probed by means of muon spin rotation. The pressure dependence (0-1 GPa) of the basal-plane magnetic penetration depth (λ_a), the penetration depth anisotropy (γ=λ_c/λ_a) and the temperature dependence of 1/λ_i^2 (i=a,c) were studied in single crystals. A strong decrease of λ_a with pressure was observed, while γand λ_i^2(0)/λ_i^2(T) are pressure independent. A linear relationship between 1/λ_a^2(270 mK) and Tc was also found. The large decrease of λ_a with pressure is the signature of an increase of the…
The superconducting penetration depth, $λ(T)$, has been measured in RFeAsO$_{0.9}$F$_{0.1}$ (R=La,Nd) single crystals (R-1111). In Nd-1111, we find an upturn in $λ(T)$ upon cooling and attribute it to the paramagnetism of the Nd ions, similar to the case of the electron-doped cuprate Nd-Ce-Cu-O. After the correction for paramagnetism, the London penetration depth variation is found to follow a power-law behavior, $Δλ_L(T)\propto T^{2}$ at low temperatures. The same $T^2$ variation of $λ(T)$ was found in non-magnetic La-1111 crystals. Analysis of the superfluid density and of penetration depth …
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 a [110] interface show a strong upturn in lambda_ab at around 7K, when the field is oriented so that the supercurrents flow around this surface. In YBCO this upturn is completely suppressed by a field of ~0.1 T…
Microscopic variations in composition or structure can lead to nanoscale inhomogeneity in superconducting properties such as the magnetic penetration depth, but measurements of these properties are usually made on longer length scales. We solve a generalized London equation with a non-uniform penetration depth, lambda(r), obtaining an approximate solution for the disorder-averaged Meissner effect. We find that the effective penetration depth is different from the average penetration depth and is sensitive to the details of the disorder. These results indicate the need for caution when interpre…
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$1.75 K for TbPdBi. Such a contrast in properties between these two compounds opens a question about the effects of band structure or magnetic correlations on superconductivity. Using the combination of a tunnel diode oscillator (TDO) and a commercial dilution refrigerator, we measured temperature dependent magnetic penetrat…
Analytical formula to evaluate the vortex-penetration field at a groove with a depth smaller than penetration depth is derived, which can be applied to surfaces of cavities or test pieces made from extreme type II superconductors such as nitrogen-doped Nb or alternative materials like Nb3Sn or NbN.
The in-plane magnetic penetration depth λ_{ab} of the iron selenide superconductor with the nominal composition FeSe_0.85 was studied by means of muon-spin rotation. The measurements of λ_{ab}^{-2}(T) are inconsistent with the presence of nodes in the gap as well as with a simple isotropic s-wave type of the order parameter, but can be equally well described within a two-gap (s+s) and an anisotropic s-wave gap picture. This implies that the superconducting energy gap in FeSe_0.85 contains no nodes.
Temperature and magnetic field dependent measurements of the microwave surface impedance of superconducting LaFeAsO$_{0.9}$F$_{0.1}$ (\Tc $\approx$ 26K) reveal a very large upper critical field ($B_{\rm c2} \approx 56$T) and a large value of the depinning frequency ($f_{0}\approx 6$GHz); together with an upper limit for the effective London penetration depth, $λ_{\rm eff} \le 200 \rm nm$, our results indicate a strong similarity between this system and the high-$T_{\rm c}$ superconducting cuprates.
The low temperature variation of the London penetration depth for a number of iron-pnictide and iron-chalcogenide superconductors is nearly quadratic, $Δλ(T) = βT^n$ with $n\approx 2$. The coefficient in this dependence shows a robust scaling, $β\propto 1/T_c^3$ across different families of these materials. We associate the scaling with a strong pair-breaking. The same mechanism have recently been suggested to explain the scalings of the specific heat jump, $ΔC \propto T_c^3$, and of the slopes of the upper critical field, $dH_{c2}/dT\propto T_c$ in these materials. This suggests that thermody…
We have revisited the magnetic penetration depth data on the electron-doped cuprates Pr(2-x)Ce(x)CuO(4-y) and La(2-x)Ce(x)CuO(4-y). It is proposed that the transition between the nodal-gap-like and nodeless-gap-like behaviors upon electron-doping [see, e.g., M. Kim et al., Phys. Rev. Lett. 91, 87001 (2003)] can be due to a scattering of the quasiparticles in the d-wave superconducting state by an incipient or weak antiferromagnetic spin-density-wave. This conjecture is supported by the inelastic neutron scattering and angle-resolved photoemission experiments on some closely related electron-do…
Transverse-field muon spin relaxation rates in single crystals of the heavy-fermion superconductor PrOs4Sb12 (Tc = 1.85 K) are nearly constant in the vortex state for temperatures below ~0.5Tc. This suggests that the superconducting penetration depth lambda(T) is temperature-independent at low temperatures, consistent with a gapped quasiparticle excitation spectrum. In contrast, radiofrequency measurements yield a stronger temperature dependence of lambda(T), indicative of point nodes in the gap. A similar discrepancy exists in superconducting Sr2RuO4 which, like PrOs4Sb12, breaks time-reversa…
We report transverse field and zero field muon spin rotation studies of the superconducting rhenium oxide pyrochlore, Cd2Re2O7. Transverse field measurements (H=0.007 T) show line broadening below Tc, which is characteristic of a vortex state, demonstrating conclusively the type-II nature of this superconductor. The penetration depth is seen to level off below about 400 mK (T/Tc~0.4), with a rather large value of lambda (T=0)~7500A. The temperature independent behavior below ~ 400 mK is consistent with a nodeless superconducting energy gap. Zero-field measurements indicate no static magnetic f…
We report measurements of the magnetic penetration depth $λ$ in single crystals of PrOs$_{4}$Sb$_{12}$ down to $\sim$0.1 K using a tunnel-diode based, self-inductive technique at 21 MHz, with the ac field applied along the \textit{a}, \textit{b} and \textit{c} directions. In all three field orientations the penetration depth and superfluid density $ρ_{s}$ tend to follow a power law, $λ\sim \mathit{T}^{2}, ρ_{s} \sim \mathit{T}% ^{2}$ at low temperatures. $ρ_{s}$ for various gap functions have been calculated, and data is best fit by the $^{3}$He A-phase-like gap with multidomains, each having …
We discuss the effect of a secondary component of the superconducting order parameter on the superfluid density in the cuprates. If we assume a main $d_{x^2-y^2}$ gap, the most stable realization of a mixed order parameter has a time-reversal breaking $d_{x^2-y^2}+ \imath d_{xy}$ symmetry. In this state the nodes are removed and the temperature dependence of the superfluid density changes from the linear behavior of a pure d-wave to a more rounded shape at low temperature. The latter is compatible with the behavior experimentally observed in the in-plane magnetic field penetration depth of opt…
We report temperature- and magnetic field-dependent bulk muon spin rotation measurements in a c-axis oriented superconductor CaC6 in the mixed state. Using both a simple second moment analysis and the more precise analytical Ginzburg-Landau model, we obtained a field independent in-plane magnetic penetration depth λab (0) = 72(3) nm. The temperature dependencies of the normalized muon spin relaxation rate and of the normalized superfluid density result to be identical, and both are well represented by the clean limit BCS model with 2Δ/kB Tc = 3.6(1), suggesting that CaC6 is a fully gapped BCS …
The hole concentration (p)(delta), the transition temperature Tc, the intragrain penetration depth lambda, and the Meissner effect were measured for annealed RuSr2(Gd,Ce)2Cu2O10+delta samples. The intragrain superconducting transition temperature Tc} varied from 17 to 40 K while the p changed by only 0.03 holes/CuO2. The intragrain superfluid-density 1/lambda^2 and the diamagnetic drop of the field-cooled magnetization across Tc (the Meissner effect), however, increased more than 10 times. All of these findings are in disagreement with both the Tc vs. p and the Tc vs. 1/lambda^2 correlations p…
Efforts have been ongoing to establish superconducting spintronics utilizing ferromagnet/superconductor heterostructures1. Previously reported devices are based on spin-singlet superconductors (SSCs), where the spin degree of freedom is lost. Spin-polarized supercurrent induction in ferromagnetic metals (FMs) is achieved even with SSCs, but only with the aid of interfacial complex magnetic structures, which severely affect information imprinted to the electron spin. Use of spin-triplet superconductors (TSCs) with active spins potentially overcomes this difficulty and further leads to novel fun…
The magnetic penetration depth $λ$ has been measured in MgCNi$_{3}$ single crystals using both a high precision Tunnel Diode Oscillator technique (TDO) and Hall probe magnetization (HPM). In striking contrast to previous measurements in powders, $δλ$(T) deduced from TDO measurements increases exponentially at low temperature, clearly showing that the superconducting gap is fully open over the whole Fermi surface. An absolute value at zero temperature $λ(0)=230 $nm is found from the lower critical field measured by HPM. We also discuss the observed difference of the superfluid density deduced f…
We report measurements of London penetration depth $λ(T)$ for the noncentrosymmetric superconductor BiPd by using a tunnel diode oscillator. Pronounced anisotropic behavior is observed in the low-temperature penetration depth; the in-plane penetration depth $λ_{ac}(T)$ follows an exponential decrease, but the interplane penetration depth $λ_b(T)$ shows power-law-type behavior. The superfluid density $ρ_s(T)$, converted from the penetration depth $λ(T)$, is best fitted by an anisotropic two-band BCS model. We argue that such a complex order parameter is attributed to the admixture of spin-singl…
It is shown that the notion of the finite pairing interaction energy range $T_d$ results in a linear temperature dependence of the London magnetic penetration depth $Δλ/ λ(0) = (T/T_d)(2/π)\ln 2$ at low temperature, in the case of the s-wave pairing state.
This topical review summarizes various features of magnetic penetration depth in unconventional superconductors. Precise measurements of the penetration depth as a function of temperature, magnetic field and crystal orientation can provide detailed information about the pairing state. Examples are given of unconventional pairing in hole- and electron-doped cuprates, organic and heavy fermion superconductors. The ability to apply an external magnetic field adds a new dimension to penetration depth measurements. We discuss how field dependent measurements can be used to study surface Andreev bou…
The temperature and field dependence of the effective magnetic penetration depth in the vortex state of a d-wave superconductor, as measured by muon spin rotation experiments, is calculated using a nonlocal London model. We show that at temperatures below T^* \propto \sqrt{B}, the linear T-dependence of the effective penetration depth crosses over to a T^3-dependence. This could provide an explanation for the low temperature flattening of the effective penetration depth curves observed in a recent muon spin rotation experiment.
We investigate the magnetic penetration depth λin superconducting Ba_1-xK_xFe_2As_2 (T_c\simeq32K) with muon-spin rotation (\muSR) and angle-resolved photoemission (ARPES). Using \muSR, we find the penetration-depth anisotropy γ_λ=λ_c/λ_{ab} and the second-critical-field anisotropy γ_{H_c2} to show an opposite T-evolution below T_c. This dichotomy resembles the situation in the two-gap superconductor MgB_2. A two-gap scenario is also suggested by an inflection point in the in-plane penetration depth λ_ab around 7K. The complementarity of \muSR and ARPES allows us to pinpoint the values of the …
Based on the recent developed real-space theory of superconductivity (arXiv:0910.5511 and arXiv:1001.5067), we study the physical nature of the Meissner effect and London penetration depth in conventional and non-conventional superconductors. It is argued that they originate from an exactly the same reason of the real-space quasi-one-dimensional periodic dynamic charge stripes in the superconductors. The fundamental relationship between the London penetration depth and the superconducting electron density is qualitatively determined.
The penetration depth of anisotropic two-band s-wave superconductors have been studied by Ginzburg-Landau approach. The anisotropic spherical Fermi surfaces and order parameters with the spherical ellipse or pancake Fermi shape are used for derive penetration depth equation. The numerical calculation of pancake-pancake and pancake-ellipse Fermi sphere shape are fits well with the experiment data of MgB2 and CaAlSi superconductor, consequently. Our model should be the way to increase understanding in the microscopic mechanism of occurrence of the penetration depth in superconductivity state of …
We compute the nominal magnetic penetration depth of $R$NiO$_2$ ($R =$ La, Nd) from first principles calculations and discuss the results in relation to the superconducting $T_c$. We find a marked discrepancy with the well established phenomenology that correlates these two quantities in cuprates (Uemura plot). We also consider the 2D ultrathin limit and estimate the maximum attainable $T_c$ to be $\sim 180$ K according to the Nelson-Kosterliz universal relation between the superfluid density and the transition temperature.
We study the temperature dependence of the magnetic penetration depth in a 3D topological superconductor (TSC), incorporating the paramagnetic current due to the surface states. A TSC is predicted to host a gapless 2D surface Majorana fluid. In addition to the bulk-dominated London response, we identify a $T^3$ power-law-in-temperature contribution from the surface, valid in the low-temperature limit. Our system is fully gapped in the bulk, and should be compared to bulk nodal superconductivity, which also exhibits power-law behavior. Power-law temperature dependence of the penetration depth c…
Recent measurements of the superconducting penetration depth in Ba(Fe_1-x Co_x)2As2 appeared to disagree on the magnitude and curvature of Δλ_{ab}(T), even near optimal doping. These measurements were carried out on different samples grown by different groups. To understand the discrepancy, we use scanning SQUID susceptometry and a tunnel diode resonator to measure the penetration depth in a single sample. The penetration depth observed by the two techniques is identical with no adjustments. We conclude that any discrepancies arise from differences between samples, either in growth or crystal …
A brief discussion is given on the nonlocal effect in multigapped superconductivity. It is pointed out that the effective magnetic penetration depth at lower external fields may be reduced by the nonlocal effect associated with the presence of small energy gap. A crude estimation of the effect in double gap system is provided and compared with the data obtained by muSR in MgB2.
We report measurements of the magnetic penetration depth in YBCO films at various oxygen concentrations. At optimal doping, critical fluctuation effects are absent, and the penetration depth from 4 K to 0.99 Tc is well described by d-wave, BCS, strong-coupling theory with a gap, Delta0/ kT ~ 3.3. This implies that the T-dependence of the penetration depth comes largely from single-particle excitations. As in crystals, underdoping reduces the zero temperature superfluid density without affecting the low-T slope or curvature of the penetration depth. We show that these results, as well as heat c…
We have studied the anisotropy of the London penetration depth, which was obtained from reversible magnetization measurements with the magnetic field both parallel and perpendicular to the c-axis. The anisotropy of the London penetration depth has a smaller magnitude than the anisotropy of the upper critical field and increases with temperature while that of the upper critical field decreases as reported earlier. This behavior is in sharp contrast with the behaviors of superconductors with one superconducting energy gap. The temperature dependence of the anisotropies of the London penetration …
We have magnetically imaged interlayer Josephson vortices emerging from an ac face of single crystals of the single layer cuprate high-Tc superconductor (Hg,Cu)Ba2CuO4+d. These images provide a direct measurement of the c-axis penetration depth of about 10 microns. This length is a factor of 10 longer than predicted by the interlayer tunneling model for the mechanism of superconductivity in layered compounds, indicating that the condensation energy available through this mechanism is 100 times smaller than is required for superconductivity.
