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.
We study inelastic (dynamical) impurity scattering effects in two-band superconductors with the same ($s_{++}$ wave) or different ($s_\pm$ wave) sign order parameters. We focus on the enhancement of the superconducting transition temperature $T_{\rm c}$ by magnetic interband scattering with the interchange of crystal-field singlet ground and multiplet excited states. Either the $s_{++}$-wave or $s_\pm$-wave state is favored by the impurity-mediated pairing, which depends on the magnetic and nonmagnetic scattering strengths derived from the hybridization of the impurity states with the conducti…
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…
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…
The results of first principles calculations of the electronic structure and the electron-phonon interaction in MgB2 are used to study theoretically the temperature dependence and anisotropy of the magnetic field penetration depth. The effects of impurity scattering are essential for a proper description of the experimental results. We compare our results with experimental data and we argue that the two-band model describes the data rather well.
We present a theoretical description of the London penetration depth of a multi-band superconductor in the case when both superconducting and spin-density wave orders coexist. We focus on clean systems and zero temperature to emphasize the effect of the two competing orders. Our calculation shows that the supefluid density closely follows the evolution of the superconducting order parameter as doping is increased, saturating to a BCS value in the pure superconducting state. Furthermore, we predict a strong anisotropic in-pane penetration depth induced by the spin-density wave order.
Microscopic calculation of coherence lengths and magnetic penetration depth in multiband superconductors
The University of Tokyo（东京大学）；Tokyo Metropolitan University（东京都立大学）；Hokkaido University（北海道大学）；RIKEN Center for Emergent Matter Science（理化学研究所新兴物质科学中心）
The London model describes strongly type-2 superconductors as massive vector field theories, where the magnetic field decays exponentially at the length scale of the London penetration length. This also holds for isotropic multi-band extensions, where the presence of multiple bands merely renormalises the London penetration length. We show that, by contrast, the magnetic properties of anisotropic multi-band London models are not this simple, and the anisotropy leads to the inter-band phase differences becoming coupled to the magnetic field. This results in the magnetic field in such systems ha…
Since Ginzburg and Landau's seminal work in 1950 superconducting states have been classified by the hierarchy of the fundamental length scales of the theory; the magnetic field penetration lengths and coherence lengths. In the simplest single-component case they form a dimensionless ratio κ. As pointed out by Ginzburg in 1952, in general the ratio depends on the direction of the applied magnetic field due to material anisotropies. Single component materials can therefore display type-1 superconductivity when the field is applied in one direction and type-2 when the field is applied in a differ…
We report measurements of the London penetration depth $Δλ(T)$ and the electronic specific heat $C_e(T)$ on high-quality single crystals of the filled-skutterudite superconductor PrPt$_4$Ge$_{12}$ ($T_c\simeq$8K). Both quantities show a weak temperature dependence at $T\ll T_c$, following $Δλ\sim T^n$ ($n\simeq 3.2$) and $C_e/T\sim T^{2.8}$. Such temperature dependences deviate from both conventional s-wave type and nodal superconductivity. A detailed analysis indicates that the superfluid density $ρ_s(T)$, derived from the penetration depth, as well as the electronic specific heat can be cons…
The precise nature of unconventional superconductivity in Iron Pnictides is presently a hotly debated issue. Here, using insights from normal state electronic structure and symmetry arguments, we show how an unconventional SC emerges from the bad metal "normal" state. Short-ranged, multi-band spin- and charge correlations generates nodeless SC in the active planar $d_{xz,yz}$ bands, and an inter-band proximity effect induces out-of-plane gap nodes in the passive $d_{3z^{2}-r^{2}}$ band. While very good quantitative agreement with various key observations in the SC state and reconciliation with…
Vortices carrying fractions of a flux quantum are predicted to exist in multiband superconductors, where vortex core can split between multiple band-specific components of the superconducting condensate. Using the two-component Ginzburg-Landau model, we examine such vortex configurations in a two-band superconducting slab in parallel magnetic field. The fractional vortices appear due to the band-selective vortex penetration caused by different thresholds for vortex entry within each band-condensate, and stabilize near the edges of the sample. We show that the resulting fractional vortex config…
The temperature dependences of the plasma frequency, superfluid density and London penetration depth were determined from terahertz spectra of conductivity and dielectric permittivity of BaFe$_{1.91}$Ni$_{0.09}$As$_{2}$ film with critical temperature $T_c=19.6$~K. Part of experimental data were analyzed within a simple three-band Eliashberg model where the mechanism of superconducting coupling is mediated by antiferromagnetic spin fluctuations, whose characteristic energy $Ω_{0}$ scales with $T_{c}$ according to the empirical law $Ω_{0} = 4.65k_{B}T_{c}$, and with a total electron-boson coupli…
Measurements of the London penetration depth and tunneling conductance in single crystals of the recently discovered stoicheometric, iron - based superconductor, CaKFe$_4$As$_4$ (CaK1144) show nodeless, two effective gap superconductivity with a larger gap of about 6-9 meV and a smaller gap of about 1-4 meV. Having a critical temperature, $T_{c,onset}\approx$35.8 K, this material behaves similar to slightly overdoped Ba$_{1-x}$K$_x$)Fe$_2$As$_2$ (e.g. $x=$0.54, $T_c \approx$ 34 K)---a known multigap $s_{\pm}$ superconductor. We conclude that the superconducting behavior of stoichiometric CaK11…
In- and out-of-plane magnetic penetration depths were measured in three iron-based pnictide superconducting systems. All studied samples of both 122 systems show a robust power-law behavior, $λ(T) T^n$, with the sample-dependent exponent n=2-2.5, which is indicative of unconventional pairing. This scenario could be possible either through scattering in a $s_{\pm }$ state or due to nodes in the superconducting gap. In the Nd-1111 system, the interpretation of data may be obscured by the magnetism of rare-earth ions. The overall anisotropy of the pnictide superconductors is small. The 1111 syste…
We have studied the lower critical fields H_{c1} of superconducting iron oxipnictide PrFeAsO_{1-y} single crystals for H parallel and perpendicular to the ab-planes. Measurements of the local magnetic induction at positions straddling the sample edge by using a miniature Hall-sensor array clearly resolve the first flux penetration from the Meissner state. The temperature dependence of H_{c1} for H || c is well scaled by the in-plane penetration depth without showing any unusual behavior, in contrast to previous reports. The anisotropy of penetration lengths at low temperatures is estimated to …
The in-plane thermal conductivity of iron-based superconductor Ca$_{10}$(Pt$_{4-δ}$As$_8$)((Fe$_{1-x}$Pt$_{x}$)$_2$As$_2$)$_5$ single crystal (``10-4-8", $T_c$ = 22 K) was measured down to 80 mK. In zero field, the residual linear term $κ_0/T$ is negligible, suggesting nodeless superconducting gaps in this multiband compound. In magnetic fields, $κ_0/T$ increases rapidly, which mimics those of multiband superconductor NbSe$_2$ and LuNi$_2$B$_2$C with highly anisotropic gap. Such a field dependence of $κ_0/T$ is an evidence for multiple superconducting gaps with quite different magnitudes or hi…
The recent discovery of high-temperature superconductivity in single-layer iron selenide has generated significant experimental interest for optimizing the superconducting properties of iron-based superconductors through the lattice modification. For simulating the similar effect by changing the chemical composition due to S doping, we investigate the superconducting properties of high-quality single crystals of FeSe$_{1-x}$S$_{x}$ ($x$=0, 0.04, 0.09, and 0.11) using magnetization, resistivity, the London penetration depth, and low temperature specific heat measurements. We show that the intro…
A conventional superconductor is described by a single complex order parameter field which has two fundamental length scales, the magnetic field penetration depth λand the coherence length ξ. Their ratio κdetermines the response of a superconductor to an external field, sorting them into two categories as follows; type-I when κ<1/\sqrt{2} and type-II when κ>1/\sqrt{2} . We overview here multicomponent systems which can possess three or more fundamental length scales and allow a separate "type-1.5" superconducting state when, e.g. in two-component case ξ_1<\sqrt{2}λ<ξ_2. In that state, as a con…
We investigate the temperature dependence of the lower critical field $H_{c1}(T)$, the field at which vortices penetrate into the sample, of a high-quality fluorine-doped NdFeAsO single crystal under static magnetic fields $H$ parallel to the $c$-axis. The temperature dependence of the first vortex penetration field has been experimentally obtained and pronounced changes of the $H_{c1}$(T) curvature are observed, which is attributed to the multiband superconductivity. Using a two-band model with $s$-wave-like gaps, the temperature-dependence of the lower critical field $H_{c1}(T)$ can be well …
Key questions for any superconductor include: what is its maximum dissipation-free electrical current (its `critical current') and can this be used to extract fundamental thermodynamic parameters? Present models focus on depinning of magnetic vortices and implicate materials engineering to maximise pinning performance. But recently we showed that the self-field critical current for thin films is a universal property, independent of microstructure, controlled only by the penetration depth. Here we generalise this observation to include thin films, wires or nanowires of single- or multi-band s-w…
We present superconducting properties of single crystalline Ba(Fe$_{0.9}$Co$_{0.1}$)$_{2}$As$_{2}$ by measuring magnetization, resistivity, upper critical field, Hall coefficient, and magneto-optical images. The magnetization measurements reveal fish-tail hysteresis loop at high temperatures and relatively high critical current density above $J_{c}=10^{5}$ A/cm$^{2}$ at low temperatures. Upper critical field determined by resistive transition is anisotropic with anisotropic parameter $\sim$ 3.5. Hall effect measurements indicate that Ba(Fe$_{0.9}$Co$_{0.1}$)$_{2}$As$_{2}$ is a multiband system…
I calculated the effect of magnetic impurities on the normal and superconductive properties of a multiband s-wave superconductor by direct solution of the two-band Eliashberg equations. In this way I determined the critical temperature, the values of the superconductive gaps, the shape of the superconductive density of states and other physical quantities that depend on the concentration of magnetic impurities. I found that the gaps and the penetration lengths display an unusual behaviour as a function of temperature. I examine the possibility that the presence of a negative induced gap raises…
We report theoretical values for the unscreened plasma frequencies Omega_p of several Fe pnictides obtained from DFT based calculations within the LDA and compare them with experimental plasma frequencies obtained from reflectivity data. The sizable renormalization observed for all considered compounds points to the presence of many-body effects beyond the LDA. From the large empirical background dielectric constant of about 12-15, we estimate a large arsenic polarizability of about 9.5 +- 1.2 Angstroem^3 where the details depend on the polarizabilities of the remaining ions taken from the lit…
To probe manifestations of multiband superconductivity in oxypnictides, we measured the angular dependence of the magnetic torque $τ(θ)$ in the mixed state of LaO$_{0.9}$F$_{0.1}$FeAs single crystals as a function of temperature $T$ and magnetic fields $H$ up to 18 T. The paramagnetic contribution of the Fe ions is properly treated in order to extract the effective mass anisotropy parameter $γ=(m_c/m_{ab})^{1/2}$ from $τ(θ)$. We show that $γ$ depends strongly on both $T$ and $H$, reaching a maximum value of $\sim$ 10 followed by a decrease towards values close to 1 as $T$ is lowered. The obser…
To probe manifestations of multiband superconductivity in oxypnictides, we measured the angular dependence of magnetic torque $τ(θ)$ in the mixed state of SmO$_{0.8}$F$_{0.2}$FeAs single crystals as functions of temperature $T$ and high magnetic field $H$ up to 30 T. We show that the effective mass anisotropy parameter $γ$ extracted from $τ(θ)$, can be greatly overestimated if the strong paramagnetism of Sm or Fe ions is not properly taken into account. The correctly extracted $γ$ depends on both $T$ and $H$, saturating at $γ\simeq 9$ at lower temperatures. Neither the London penetration depth…
We investigate the temperature dependence of the lower critical field Hc1(T) of a high-quality FeSe single crystal under static magnetic fields H parallel to the c axis. The temperature dependence of the first vortex penetration field has been experimentally obtained by two independent methods and the corresponding Hc1(T) was deduced by taking into account demagnetization factors. A pronounced change in the Hc1(T) curvature is observed, which is attributed to anisotopic s-wave or multiband superconductivity. The London penetration depth λab(T) calculated from the lower critical field does not …
The superconducting pairing state of LaPt$_{4}$Ge$_{12}$ is studied by measuring the magnetic penetration depth $λ(T,B)$ and the superfluid density $ρ_s(T)$ using a tunnel-diode-oscillator (TDO)-based method and by transverse field muon-spin rotation ($μ$SR) spectroscopy. $λ(T)$ follows an exponential-type temperature dependence at $T\ll T_{c}$, but its zero-temperature value $λ(0)$ increases linearly with magnetic field. Detailed analyses demonstrate that both $λ(T)$ and the corresponding $ρ_{s}(T)$, measured in the Meissner state by the TDO method are well described by a two-gap $γ$ model wi…
The superconducting properties of the recently discovered double Fe$_2$As$_2$ layered high-$T_c$ superconductor RbCa$_2$Fe$_4$As$_4$F$_2$ with $T_c\approx$ 30~K have been investigated using magnetization, heat capacity, transverse-field (TF) and zero-field (ZF) muon-spin rotation/relaxation ($μ$SR) measurements. Our low field magnetization measurements and heat capacity (C$_p$) reveal an onset of bulk superconductivity with $T_{\bf c}\sim$ 30.0(4) K. Furthermore, the heat capacity exhibits a jump at $T_{\bf c}$ of $Δ$C$_p$/$T_{\bf c}$=94.6 (mJ/mole-K$^2$) and no clear effect of applied magneti…
We have investigated the superconducting ground state of the newly discovered superconductor ThFeAsN with a tetragonal layered crystal structure using resistivity, magnetization, heat capacity and transverse-field (TF) muon-spin rotation ($μ$SR) measurements. Our resistivity and magnetization measurements reveal an onset of bulk superconductivity with $T_{\bf c}\sim$ 30 K. The heat capacity results show a very small anomaly, $Δ$C$_{ele}$$\sim$0.214 (J/mol-K) at $T_{\bf c}\sim$ 30 K and exhibits exponential behavior below $T_{\bf c}$, which fits better to two superconducting gaps rather than a …
