Multigap Superconductivity Research Articles

Anomalous Josephson vortex solutions in Josephson junctions with multiple tunneling channels

We construct a theory for Josephson junction with multiple tunneling channels. We focus on two situations, i.e., a heterotic junction composed of two-gap-superconductor, insulator, and one-gap-superconductor, and a grain-boundary junction formed by two identical multi-gap superconductors. Then, we show that the magnetic field distribution of the Josephson vortex for ±s-wave superconductivity is much more enlarged than that for s-wave without sign change between the order parameters. We display such anomalous vortices and suggest how to evaluate the enlargement.

Multiband conductivity and a multigap superconducting phase inV3Sifilms from optical measurements at terahertz frequencies

The possibility of multiband conductivity and multigap superconductivity is explored in oriented ${\text{V}}_{3}\text{Si}$ thin films by means of reflectance and transmittance measurements at terahertz frequencies. The temperature dependence of the transmittance spectra in the normal state gives evidence of two bands contributing to the film conductivity. This outcome is consistent with electronic structure calculations performed within density functional theory. On this basis, we performed a detailed data analysis and found that all optical data can be consistently accounted for within a two-band framework, with the presence of two optical gaps in the superconducting state corresponding to $2\ensuremath{\Delta}/k{T}_{c}$ values close to 1.8 and 3.8.

Superconductivity from a non-Fermi-liquid metal: Kondo fluctuation mechanism in slave-fermion theory

We find new mechanism of superconductivity beyond the spin-fluctuation theory, the standard model for unconventional superconductivity in the weak coupling approach, where Kondo fluctuations result in multi-gap superconductivity around an antiferromagnetic quantum critical point of the slave-fermion theory. Fingerprints of the hybridization mechanism are two kinds of resonance modes in not only spin but also charge fluctuations, originating from $d-wave$ pairing of conduction electrons and spinless holons, respectively, thus differentiated from the spin-fluctuation mechanism. We show that the ratio between each superconducting gap for conduction electrons $\Delta_{c}$ and holons $\Delta_{f}$ and the transition temperature $T_{c}$ is $2\Delta_{c} / T_{c} \sim 9$ and $2\Delta_{f} / T_{c} \sim \mathcal{O}(10^{-1})$, remarkably consistent with $CeCoIn_{5}$.

Theory of vortex structure in Josephson junctions with multiple tunneling channels: Vortex enlargement as a probe of±s-wave superconductivity

We theoretically study Josephson vortex structures in Josephson junctions which have multiple tunneling channels caused by multiple superconducting gaps. Deriving ``coupled sine-Gordon equations'' from the free-energy taking account of the multiple tunneling channels, we examine two typical situations, a heterotic junction composed of multigap-superconductor, insulator, and single-gap superconductor, and a grain-boundary junction formed by two identical multigap superconductors. Then, we reveal in both situations that the magnetic field distribution of the Josephson vortex for $\ifmmode\pm\else\textpm\fi{}s$-wave superconductivity is more enlarged than that for $s$ wave without sign change between the order parameters. Its mechanism is ascribed to a cancellation of the multiple Josephson currents. We display such an anomalous Josephson vortex and suggest how to evaluate the enlargement.

Misfit Strain in Superlattices Controlling the Electron-Lattice Interaction via Microstrain in Active Layers

High-temperature superconductivity (HTS) emerges in quite different electronic materials: cuprates, diborides, and iron-pnictide superconductors. Looking for unity in the diversity we find in all these materials a common lattice architecture: they are practical realizations of heterostructures at atomic limit made of superlattices of metallic active layers intercalated by spacers as predicted in 1993 by one of us. The multilayer architecture is the key feature for the presence of electronic topological transitions where the Fermi surface of one of the subbands changes dimensionality. The superlattice misfit strain between the active and spacer layers is shown to be a key variable to drive the system to the highest critical temperature that occurs at a particular point of the 3D phase diagram () where is the charge transfer or doping. The plots of as a function of misfit strain at constant charge transfer in cuprates show a first-order quantum critical phase transition where an itinerant striped magnetic phase competes with superconductivity in the proximity of a structural phase transition, that is, associated with an electronic topological transition. The shape resonances in these multigap superconductors is associated with the maximum .

Thermal conductivity measurements of the energy-gap anisotropy of superconducting LaFePO at low temperatures

The superconducting gap structure of LaFePO $({T}_{c}=7.4\text{ }\text{K})$ is studied by thermal conductivity $(\ensuremath{\kappa})$ at low temperatures in fields $H$ parallel and perpendicular to the $c$ axis. A clear two-step field dependence of $\ensuremath{\kappa}(H)$ with a characteristic field ${H}_{s}(\ensuremath{\sim}350\text{ }\text{Oe})$ much lower than the upper critical field ${H}_{c2}$ is observed. In spite of the large anisotropy of ${H}_{c2}$, $\ensuremath{\kappa}(H)$ in both $H$ directions is nearly identical below ${H}_{s}$. Above ${H}_{s}$, $\ensuremath{\kappa}(H)$ grows gradually with $H$ with a convex curvature, followed by a steep increase with strong upward curvature near ${H}_{c2}$. These results indicate multigap superconductivity with active two-dimensional (2D) and passive three-dimensional bands having contrasting gap values. Together with the recent penetration depth results, we suggest that the 2D bands consist of nodal and nodeless ones, consistent with extended $s$-wave symmetry.

Superconducting anisotropy in single-crystalline Ba(Fe0.93Co0.07)2As2 near Tc

The superconducting anisotropy γ has been studied on single-crystalline Ba(Fe0.93Co0.07)2As2(Tc=22.5K) at temperatures T⩾20K and fields H⩽10T by measuring magnetic torque τ as a function of angle θ between the c axis and the H direction. The reversible part in τ(θ) can be well-described with γ=3–3.5, which is almost T and H independent within the measurement range. The result manifests that this material, known as the multigap superconductor, behaves as a simple anisotropic superconductor at least near Tc. The irreversible part in τ(θ) shows broad peak at θ=90°, indicating the absence of strong layer pinning.

Intergrain Josephson Currents in Multigap Superconductors: Microscopic Origin of Low Intergrain Critical Current and Its Recovery Potential in Iron-Pnictide Materials

We microscopically examine the intergrain Josephson current in iron-pnictide superconductors in order to solve the puzzle of why the intergrain current is much lower than the intragrain one. The theory predicts that the intergrain Josephson current is significantly reduced by the $\pm$s-wave symmetry when the incoherent tunneling becomes predominant and the density of states and the gap amplitude between two bands are identical. We find in such a situation that the temperature dependence of the intergrain Josephson current shows an anomalously flat curve over a wide temperature range. Finally, we suggest important points for increasing the intergrain current.

Nodal superconductivity and antinodal pseudogap in cuprate superconductors

According to recent experimental findings the leading pairing resides in the nodal (FS arcs) momentum region of hole doped cuprates. The pseudogap is an antinodal feature. A corresponding multiband model of the electronic background evolving with doping serves the usually presented phase diagram. The pairing is due by the pair-transfer between overlapping nodal defect (polaron) band and the itinerant band. A bare gap vanishing with extended doping between the antinodal defect subband and the itinerant band top leads to the formation of the pseudogap as a perturbative band-structure effect. The calculated behaviour of two superconducting gaps and of the pseudogap on the whole doping scale is in qualitative agreement with the observations. Arguments to include cuprates into the class of multiband–multigap superconductors are given by these results.

Superconductivity in Fe and As Based Compounds: A Bridge Between MgB2 and Cuprates

By interpreting various experimental data for the new high temperature FeAs type superconductors in terms of lattice mediated multigap superconductivity, it is shown that these systems strongly resemble MgB2, however, with the distinction that local polaronic lattice effects exist. This fact establishes a connection to cuprate high temperature superconductors where polaron formation is essential for the pseudogap phase and the unconventional isotope effects observed there. However, similarly to MgB2 and in contrast to cuprates, the two superconducting gaps in the Fe-As based materials are isotropic s-wave gaps.

Nonexponential London penetration depth of external magnetic fields in superconductingBa1−xKxFe2As2single crystals

We have studied the in- and out-of-plane magnetic penetration depths in the hole-doped iron-based superconductor ${\text{Ba}}_{1\ensuremath{-}x}{\text{K}}_{x}{\text{Fe}}_{2}{\text{As}}_{2}\text{ }({T}_{c}\ensuremath{\approx}30\text{ }\text{K})$. Single crystals grown from different fluxes and by different groups showed nearly identical results. The in-plane London penetration depth ${\ensuremath{\lambda}}_{ab}$ is not exponentially saturating at low temperature, as would be expected from a fully gapped superconductor. Instead, ${\ensuremath{\lambda}}_{ab}(T)$ shows a power-law behavior, $\ensuremath{\lambda}\ensuremath{\propto}{T}^{n}\text{ }(n\ensuremath{\approx}2)$, down to $T\ensuremath{\approx}0.02{T}_{c}$, similar to the electron-doped $\text{Ba}{({\text{Fe}}_{1\ensuremath{-}x}{\text{Co}}_{x})}_{2}{\text{As}}_{2}$. The penetration depth anisotropy ${\ensuremath{\gamma}}_{\ensuremath{\lambda}}={\ensuremath{\lambda}}_{c}(T)/{\ensuremath{\lambda}}_{ab}(T)$ increases upon cooling, opposite to the trend observed in the anisotropy of the upper critical field, ${\ensuremath{\gamma}}_{\ensuremath{\xi}}={H}_{c2}^{\ensuremath{\perp}c}(0)/{H}_{c2}^{\ensuremath{\parallel}c}(0)$. These are universal characteristics of both the electron- and hole-doped 122 systems, suggesting unconventional multigap superconductivity. The behavior of the in-plane superfluid density ${\ensuremath{\rho}}_{ab}(T)$ is discussed in light of existing theoretical models proposed for the iron pnictide superconductors.

A Possible Mechanism for Evading Temperature Quantum Decoherence in Living Matter by Feshbach Resonance

A new possible scenario for the origin of the molecular collective behaviour associated with the emergence of living matter is presented. We propose that the transition from a non-living to a living cell could be mapped to a quantum transition to a coherent entanglement of condensates, like in a multigap BCS superconductor. Here the decoherence-evading qualities at high temperature are based on the Feshbach resonance that has been recently proposed as the driving mechanism for high Tc superconductors. Finally we discuss how the proximity to a particular critical point is relevant to the emergence of coherence in the living cell.

Multiband superconductivity in Pb, H under pressure and CaBeSi from ab initiocalculations

Superconductivity in Pb, H under extreme pressure and CaBeSi, in the framework of thedensity functional theory for superconductors, is discussed. A detailed analysis on how theelectron–phonon and electron–electron interactions combine together to determine thesuperconducting gap and critical temperature of these systems is presented. Pb, Hunder pressure and CaBeSi are multigap superconductors. We will address thequestion under which conditions does a system exhibits this phenomenon. Thepresented results contribute to the understanding of multiband and anisotropicsuperconductivity, which has received a lot of attention since the discovery ofMgB2, and show how it is possible to describe the superconducting properties of real materials ona fully ab initio basis.

Penetration depth, lower critical fields, and quasiparticle conductivity in Fe-arsenide superconductors

In this article, we review our recent studies of microwave penetration depth, lower critical fields, and quasiparticle conductivity in the superconducting state of Fe-arsenide superconductors. High-sensitivity microwave surface impedance measurements of the in-plane penetration depth λ ab in single crystals of electron-doped PrFeAsO 1 - y ( y ∼ 0.1 ) and hole-doped Ba 1 - x K x Fe 2 As 2 ( x ≈ 0.55 ) are presented. In clean crystals of Ba 1 - x K x Fe 2 As 2 , as well as in PrFeAsO 1 - y crystals, the penetration depth shows flat temperature dependence at low temperatures, indicating that the superconducting gap opens all over the Fermi surface. The temperature dependence of superfluid density λ ab 2 ( 0 ) / λ ab 2 ( T ) in both systems is most consistent with the existence of two different gaps. In Ba 1 - x K x Fe 2 As 2 , we find that the superfluid density is sensitive to degrees of disorder inherent in the crystals, implying unconventional impurity effect. We also determine the lower critical field H c 1 in PrFeAsO 1 - y by using an array of micro-Hall probes. The temperature dependence of H c 1 saturates at low temperatures, fully consistent with the superfluid density determined by microwave measurements. The anisotropy of H c 1 has a weak temperature dependence with smaller values than the anisotropy of upper critical fields at low temperatures, which further supports the multi-gap superconductivity in Fe-arsenide systems. The quasiparticle conductivity shows an enhancement in the superconducting state, which suggests the reduction of quasiparticle scattering rate due to the gap formation below T c . From these results, we discuss the structure of the superconducting gap in these Fe-arsenides, in comparison with the high- T c cuprate superconductors.

Multigap superconductivity in heavy fermion systems

Heavy fermion superconductors are largely studied for their unconventional ground states. We present results on the skutterudite compound PrOs4Sb12 (Tc ≈ 1.8K), and on the heavy-fermion CeCoIn5 (Tc ≈ 2.3K), where both the low field and the low temperature behaviour of their thermal conductivity yield evidence for multigap superconductivity.

Topological objects in two-gap superconductor

We discuss the non-Abelian topological objects, in particular the non-Abrikosov vortex and the magnetic knot made of the twisted non-Abrikosov vortex, in two-gap superconductor. We show that there are two types of non-Abrikosov vortex in Ginzburg-Landau theory of two-gap superconductor, the D-type which has no concentration of the condensate at the core and the N-type which has a non-trivial profile of the condensate at the core, under a wide class of realistic interaction potential. We prove that these non-Abrikosov vortices can have either integral or fractional magnetic flux, depending on the interaction potential. We show that they are described by the non-Abelian topology π2(S 2) and π1(S 1), in addition to the well-known Abelian topology π1(S 1). Furthermore, we discuss the possibility to construct a stable magnetic knot in two-gap superconductor by twisting the non-Abrikosov vortex and connecting two periodic ends together, whose knot topology π3(S 2) is described by the Chern-Simon index of the electromagnetic potential. We argue that similar topological objects may exist in multi-gap or multi-layer superconductors and multi-component Bose-Einstein condensates and superfluids, and discuss how these topological objects can be constructed in MgB2, Sr2RuO4, 3He, and liquid metallic hydrogen.

Multigap Superconductivity in Heavy Fermion Systems

Heavy fermion superconductors are largely studied for the rich variety of their unconventional ground states. But the discovery of new Pr and Ce based systems which are superconducting at zero pressure, revealed multigap effects with a remarkably low “critical field scale H c 2 S for the small gap band (of order H c 2 /100). We present results on the skutterudite heavy-fermion compound PrOs 4 Sb 12 ( T c ≈1.8 K), where both the low field and the low temperature behavior of its thermal conductivity yield evidence for multigap superconductivity as well as new ongoing results on CeCoIn 5 ( T c ≈2.3 K). Although the proximity of this last system to a quantum critical point prevents quantitative analysis of the values of the gaps as in PrOs 4 Sb 12 , it shows even stronger multigap effects ( H c 2 S ≈ H c 2 /1000...), backing the ideas that the multiband behavior is intimately related to the role of the f electrons in the pairing mechanism.

Anisotropic superconductivity in NbSe2 probed by magnetic penetration depth

NbSe2 shows coexistence of a charge density wave (TCDW∼32K) with a superconducting state below T=7.2K. Recent ARPES measurements revealed different values of the superconducting gap on the main sheets of the Fermi surface. These results suggest a multigap superconductivity such as in MgB2. The temperature dependence of the magnetic penetration depth (λ(T)) down to Tc/16 has been measured on high quality single crystals in the Meissner state. A strong increase of the in-plane penetration depth is observed, signaling the presence of low lying excitations. Given the relative contributions of each Fermi surface sheet, these measurements indicate that a reduced gap is not necessarily only found on the small Se sheet as suggested by the ARPES measurements. These results are discussed in a framework of multigap superconductivity.

Multigap Superconductivity in Y2C3: A 13C-NMR Study

We report on the superconducting (SC) properties of Y$_2$C$_3$ with a relatively high transition temperature $T_{\rm c}=15.7$ K investigated by $^{13}$C nuclear-magnetic-resonance (NMR) measurements under a magnetic field. The $^{13}$C Knight shift has revealed a significant decrease below $T_{\rm c}$, suggesting a spin-singlet superconductivity. From an analysis of the temperature dependence of the nuclear spin-lattice relaxation rate $1/T_1$ in the SC state, Y$_2$C$_3$ is demonstrated to be a multigap superconductor that exhibits a large gap $2\Delta/k_{\rm B}T_{\rm c}=5$ at the main band and a small gap $2\Delta/k_{\rm B}T_{\rm c}=2$ at other bands. These results have revealed that Y$_2$C$_3$ is a unique multigap s-wave superconductor similar to MgB$_2$.

Bulk Evidence for Single-Gaps-Wave Superconductivity in the Intercalated Graphite SuperconductorC6Yb

We report measurements of the in-plane electrical resistivity rho and thermal conductivity kappa of the intercalated graphite superconductor C6Yb down to temperatures as low as Tc/100. When a field is applied along the c axis, the residual electronic linear term kappa0/T evolves in an exponential manner for Hc1<H<Hc2/2. This activated behavior is compelling evidence for an s-wave order parameter, and is a strong argument against the possible existence of multigap superconductivity.