Isotropic Superconductors Research Articles

Effective Ginzburg–Landau free energy functional for multi-band isotropic superconductors

It has been shown that interband mixing of gradients of two order parameters (drag effect) in an isotropic bulk two-band superconductor plays important role – such a quantity of the intergradients coupling exists that the two-band superconductor is characterized with a single coherence length and a single Ginzburg–Landau (GL) parameter. Other quantities or neglecting of the drag effect lead to existence of two coherence lengths and dynamical instability due to violation of the phase relations between the order parameters. Thus so-called type-1.5 superconductors are impossible. An approximate method for solving of set of GL equations for a multi-band superconductor has been developed: using the result about the drag effect it has been shown that the free-energy functional for a multi-band superconductor can be reduced to the GL functional for an effective single-band superconductor.

Scaling rules for critical current density in anisotropic biaxial superconductors

Recent researches highlight the additional anisotropic crystallographic axis within the superconducting plane of high temperature superconductors (HTS), demonstrating the superconducting anisotropy of HTS is better understood in the biaxial frame than the previous uniaxial coordinates within the superconducting layer. To quantitatively evaluate the anisotropy of flux pinning and critical current density in HTS, we extend the scaling rule for single-vortex collective pinning in uniaxial superconductors to account for flux-bundle collective pinning in biaxial superconductors. The scaling results show that in a system of random uncorrected point defects, the field dependence of the critical current density is described by a unified function with the scaled magnetic field of the isotropic superconductor. The obtained angular dependence of the critical current density depicts the main features of experimental observations, considering possible corrections due to the strong-pinning interaction.

Effect of Surface Roughness on the Magnetic Field Profile in the Meissner State of a Superconductor

It is well known that the London model (valid for a hard type II superconductor) predicts an externally applied magnetic field decays exponentially as a function of depth into the superconductor on a length scale λ. Direct measurements of the field profile using low energy μSR on high-Tc superconductors, such as YBa2Cu3 O x measure deviations from a simple exponential decay. In particular, there is a short length scale δ close to the surface where the magnetic field does not decay. It has been proposed that this is due to surface roughness, which leads to a suppression of the order parameter near the surface. A model of surface roughness has been studied for the case of a sinusoidally modulated surface roughness on an isotropic superconductor showing that in some cases the profiles resulting from surface roughness may be qualitatively similar to the dead layer phenomena in that the field magnitude decay rate may be slowed near the surface relative to a flat interface but that for modest roughness, the quantitative value of the length over which the field decay is slowed is much smaller than the experiments measure. In this paper, we extend this work in two directions: firstly, by using atomic force microscopy data of YBa2Cu3 O x crystals, we predict the expected field profiles within the context of the Isotropic London model of superconductivity given their actual surface geometry; and secondly, we consider how surface roughness could affect experimental values for λ and δ. The main finding is that roughness within an isotropic model does not produce the dead layers found in experiments on YBa2Cu3 O x . However, we suggest that roughness in a highly anisotropic superconductor could account for the observed dead layer.

Electron doping dependence of the anisotropic superconductivity inBaFe2−xNixAs2

The upper critical field ${H}_{c2}$ in superconducting ${\mathrm{BaFe}}_{2\ensuremath{-}x}{\mathrm{Ni}}_{x}{\mathrm{As}}_{2}$ single crystals has been determined by magnetotransport measurements down to 0.6 K over the whole superconducting dome with $0.065\ensuremath{\le}x\ensuremath{\le}0.22$ for both the interplane $(H\ensuremath{\parallel}c,{H}_{c2}^{c})$ and in-plane $(H\ensuremath{\parallel}ab,{H}_{c2}^{ab})$ field directions in static magnetic fields up to 16 T and pulsed magnetic fields up to 60 T. The temperature dependence of ${H}_{c2}^{ab}$ follows the Werthamer-Helfand-Hohenberg model incorporating orbital and spin paramagnetic effects, while ${H}_{c2}^{c}(T)$ can only be described by the effective two-band model with unbalanced diffusivity. The anisotropy of the upper critical fields, $\ensuremath{\gamma}(T)={H}_{c2}^{ab}/{H}_{c2}^{c}$, monotonically increases with increasing temperature for all dopings, and its zero-temperature limit $\ensuremath{\gamma}(0)$ has an asymmetric doping dependence with a significant enhancement in the overdoped regime, where the optimally doped compound has the most isotropic superconductivity. Our results suggest that the anisotropy in the superconductivity of iron pnictides is determined by the topology of the Fermi surfaces together with the doping-induced impurity scattering.

Effects of Size, deGennes and Ginzburg–Landau Parameters on the Magnetic Susceptibility of an Isotropic Superconductor

The magnetic signature of a nanoscopic superconductor immersed in a magnetic applied field \(H_e\) is calculated numerically. The calculated magnetic susceptibility \(\partial M / \partial H_e\) of a superconducting nanoprism shows discontinuities and a quasiperiodic modulation at the vortex transition fields \(H_\mathrm{T}\) (fields for which one or several vortices enter/leave the sample). In this contribution, we studied the influence of the sample size, the Ginzburg–Landau parameter \(\kappa \) and the deGennes parameter b on the magnetic susceptibility in a type-II isotropic superconductor. We found distinct signatures of the magnetic susceptibility when superconducting samples of two and three dimensions are considered.

Zero-bias anomaly in p-wave superconductor

It was shown some time ago that a magnetic field penetrates a triplet non-chiral superconductor described by the (three-dimensional) vector order parameter as an array of magnetic skyrmions, a texture carrying two units of magnetic flux. Magnetic skyrmions do not have a normal core in contrast to Abrikosov vortices. The spectrum of Andreev midgap states of this coreless topological defect in p-wave isotropic superconductors with single parabolic band is calculated. It is shown that a magnetic field can be used to tune the Andreev state energy precisely to zero (these states are not topologically protected). They can be further stabilized and manipulated by pinning of the skyrmions on columnar defects or nanoholes. In contrast to Majorana modes in chiral p-wave superconductor, the tunneling between ZES within neighboring skyrmions is prohibited due to their high angular momentum. Experimental signatures of these states are discussed.

Pairing Symmetry Model of the Novel LaNiAsO0.7 Superconductor Studied via Fe Impurity Substitution

LaNiAsO0.7 is a novel superconductor (Tc = 4.1 K) that emerged very recently. Its pairing symmetry model was studied via Fe impurity substitution effects on the structural, magnetic, and electrical properties. The successful doping of Fe level in LaNi1−xFexAsO0.7 up to x = 0.05 results in a continuous suppression of Tc toward zero, which however is far from that expected from a pairing-breaking effect, x = 0.0029. The results evidently exclude the d-wave model. Alternatively, they likely indicate LaNiAsO0.7 as a fully gapped isotropic s-wave or multiband superconductor. The study provides fresh insights into pairing symmetry model of LaNiAsO and hence distinguishes it from the doped LaFeAsO superconductor.

Fracture analysis of a transversely isotropic high temperature superconductor strip based on real fundamental solutions

Real fundamental solution for fracture problem of transversely isotropic high temperature superconductor (HTS) strip is obtained. The superconductor E–J constitutive law is characterized by the Bean model where the critical current density is independent of the flux density. Fracture analysis is performed by the methods of singular integral equations which are solved numerically by Gauss–Lobatto–Chybeshev (GSL) collocation method. To guarantee a satisfactory accuracy, the convergence behavior of the kernel function is investigated. Numerical results of fracture parameters are obtained and the effects of the geometric characteristics, applied magnetic field and critical current density on the stress intensity factors (SIF) are discussed.

Finding the boson-number distributions in superconducting thin-film rings

A theory of the infrared (IR)-field-induced single-photon generation by the narrow thin-film superconducting rings made of the isotropic s-wave pairing type-II superconductors is presented. It is shown that statistical measurements of the energies of photons emitted by the same current-carrying ring prepared initially in the same quantum state, allow to find the number distribution of Cooper pairs in the superconductor.

Isotropic multi-gap superconductivity in BaFe1.9Pt0.1As2 from thermal transport and spectroscopic measurements

Thermal conductivity, point contact spectroscopy, angle-resolved photoemission and Raman spectroscopy measurements were performed on BaFe1.9Pt0.1As2 single crystals obtained from the same synthesis batch in order to investigate the superconducting energy gap structure using multiple techniques. Low temperature thermal conductivity was measured in the superconducting state as a function of temperature and magnetic field, revealing an absence of quasiparticle excitations in the limit up to 15 T applied magnetic fields. Point-contact Andreev reflection spectroscopy measurements were performed as a function of temperature using the needle-anvil technique, yielding features in the conductance spectra at both 2.5 meV and 7.0 meV scales consistent with a multi-gap scenario. Angle-resolved photoemission spectroscopy probed the electronic band structure above and below the superconducting transition temperature of Tc = 23 K, revealing an isotropic gap of magnitude meV on both electron and hole pockets. Finally, Raman spectroscopy was used to probe quasiparticle excitations in multiple channels, showing a threshold energy scale of 3 meV below Tc. Overall, we find strong evidence for an isotropic gap structure with no nodes or deep minima in this system, with a 3 meV magnitude gap consistently observed and a second, larger gap suggested by point-contact spectroscopy measurements. We discuss the implications that the combination of these results reveal about the superconducting order parameter in the BaFe2−xPtxAs2 doping system and how this relates to similar substituted iron pnictides.

Isotropic round-wire multifilament cuprate superconductor for generation of magnetic fields above 30 T

Magnets are the principal market for superconductors, but making attractive conductors out of the high-temperature cuprate superconductors (HTSs) has proved difficult because of the presence of high-angle grain boundaries that are generally believed to lower the critical current density, J(c). To minimize such grain boundary obstacles, HTS conductors such as REBa2Cu3O(7-x) and (Bi, Pb)2Sr2Ca2Cu3O(10-x) are both made as tapes with a high aspect ratio and a large superconducting anisotropy. Here we report that Bi2Sr2CaCu2O(8-x) (Bi-2212) can be made in the much more desirable isotropic, round-wire, multifilament form that can be wound or cabled into arbitrary geometries and will be especially valuable for high-field NMR magnets beyond the present 1 GHz proton resonance limit of Nb3Sn technology. An appealing attribute of this Bi-2212 conductor is that, being without macroscopic texture, it contains many high-angle grain boundaries but nevertheless attains a very high J(c) of 2,500 A mm(-2) at 20 T and 4.2 K. The large potential of the conductor has been demonstrated by building a small coil that generated almost 2.6 T in a 31 T background field. This demonstration that grain boundary limits to high Jc can be practically overcome underlines the value of a renewed focus on grain boundary properties in non-ideal geometries.

Superconducting properties of the ternary transition-metal silicide Zr2Ru3Si4

Superconducting properties of the polycrystalline Zr2Ru3Si4 were investigated by measuring the electrical resistivity, magnetization and specific heat. By these measurements, bulk superconductivity with transition temperature Tc = 5.5 K was confirmed. Moreover, Zr2Ru3Si4 was found to be a type-II and intermediate-coupling superconductor. Interestingly, the electronic specific heat shows a deviation from a one-gap s-wave model and Hc2(T) shows unusual positive curvature in the vicinity of Tc. The electronic structure calculation shows the existence of plural anisotropic Fermi surfaces. These results suggest that Zr2Ru3Si4 is not an isotropic single-gap superconductor, but possibly a multi-gap or an anisotropic gap superconductor.

Vortex Molecules in Thin Films of Layered Superconductors

Both the equilibrium and transport properties of the vortex matter are essentially affected by the behavior of the intervortex interaction potential. In isotropic bulk superconductors this potential is well known to be repulsive and is screened at intervortex distances R greater than the London penetration depth λ. As a result, in perfect crystals quantized Abrikosov vortices form a triangular lattice. In thin films of anisotropic superconductors this standard interaction potential behavior appears to be strongly modified because of the interplay between the long-ranged repulsion predicted in the pioneering work by J. Pearl and the attraction caused by the tilt of the vortex lines with respect to the anisotropy axes. This interplay results in a new type of vortex arrangement formed by finite-size vortex chains, i.e., vortex molecules. Tilted vortices with such unusual interaction potential form clusters with the size depending on the field tilting angle and film thickness or/and can arrange into multiquanta flux lattice. The magnetic flux through the unit cells of the corresponding flux line lattices equals to an integer number N of flux quanta. Thus, the increase in the field tilting (or varying temperature) should be accompanied by the series of the phase transitions between the vortex lattices with different N. A similar scenario should be realized in strongly anisotropic BSCCO high-T c superconductors where in tilted field a crossing lattice of Abrikosov vortices (the stacks of pancakes in this case) and Josephson vortices appears. This crossing leads to the zigzag deformation of the pancakes stacks which is responsible for the attraction interaction competing with the long-ranged Pearl’s repulsion.

Interplay of Superconductivity and Topological Order in HgTe Quantum Wells

Using the microscopic tight-binding equations we derive the effective Hamiltonian for the double-layer comprised of the two-dimensional topological insulator (TI) coupled to the s-wave isotropic superconductor (SC), and show that it contains terms describing mixing of the TI subband branches by the superconducting correlations induced by the proximity effect. We find that the proximity effect breaks down the rotational symmetry of the TI spectrum. We show that the edge states not only acquire the gap, as follows from the standard theory, but can also become localized by the Andreev-backscattering mechanism in a small coupling regime. In a strong coupling regime the edge states merge with the bulk states, and the TI transforms into an anisotropic narrow-gap semiconductor.

Orientation peculiarities of dc Josephson tunneling betweend-wave superconductors with charge density waves

The theory of the stationary Josephson tunnel current Ic was devised for junctions involving superconductors partially gapped by biaxial or unidirectional charge density waves (CDWs) and possessing a superconducting order parameter of d-wave symmetry. Specific calculations were carried out for symmetric junctions between two identical CDW superconducting electrodes and nonsymmetric ones composed of a CDW superconductor and a conventional isotropic s-wave superconductor. Two kinds of superconducting pairing symmetries were studied, namely, that appropriate to cuprates (dx2−y2) and the dxy one. The corresponding calculations were also carried out for the extended s-wave symmetry of the superconducting order parameter. Allowances were made for the directionality of tunneling. In all the cases studied, the dependences of Ic on the angle γ between the chosen crystal direction and the normal to the junction plane were found to be significantly influenced by CDWs. It was shown in particular that the d-wave driven periodicity of Ic(γ) in the CDW-free case is transformed into double-period beatings depending on the parameters of the system. The results of calculations testify that the orientation-dependent patterns Ic(γ) measured for CDW superconductors allow the CDW configuration (unidirectional or checkerboard) and the symmetry of superconducting order parameter to be determined. The predicted effects can be used to indirectly reveal CDWs in underdoped cuprates where pseudogaps are observed. The break-junction technique is an appropriate tool for this purpose.

Weak-coupling superconductivity in electron-doped NaFe0.95Co0.05As revealed by ARPES

We report a systematic study on the electronic structure and superconducting (SC) gaps in electron-doped NaFe${}_{0.95}$Co${}_{0.05}$As superconductor using angle-resolved photoemission spectroscopy. Holelike Fermi sheets are at the zone center and electronlike Fermi sheets are at the zone corner, and are mainly contributed by $xz$ and $yz$ orbital characters. Our results reveal a $\frac{\ensuremath{\Delta}}{{K}_{B}{T}_{c}}$ in the range of 1.8--2.1, suggesting a weak-coupling superconductivity in these compounds. Gap closing above the transition temperature (${T}_{c}$) shows the absence of pseudogaps. Gap evolution with temperature follows the BCS gap equation near the $\ensuremath{\Gamma}$, $Z$, and $M$ high symmetry points. Furthermore, an almost isotropic superconductivity along the ${k}_{z}$ direction in the momentum space is observed by varying the excitation energies.

Evidence of Inhomogeneous Superconductivity in FeTe1-xSexby Scotch-Tape Method

We have fabricated thin films of FeTe$_{1-x}$Se$_x$ using a scotch-tape method. The superconductivities of the thin films are different from each other although these films were fabricated from the same bulk sample. The result clearly presents the inhomogeneous superconductivity in FeTe$_{1-x}$Se$_x$. The difference comes from inhomogeneity due to the excess Fe concentration. The resistivity of a thin film with low excess Fe shows good superconductivity with the sharp superconducting-transition width and more isotropic superconductivity.

Effect of strain on critical magnetic field in type-II superconductors

The strain effect on critical magnetic field in isotropic high-κ superconductors is studied theoretically in this paper. Based on the phenomenological theory, we obtain the critical magnetic field in the presence of the applied strain. The dependence of upper critical magnetic field on the coupling parameters is discussed. The theoretical analysis is in broad agreement with experimental results as the coupling parameters are the linear functions of the strain. Furthermore, according to the assumption, the plot of strain effect on lower critical field is observed as symmetric curve for compressive and tensile strains. The plots also predict that the strain effect on lower critical field is greater in higher-κ superconductors.

Observation of an isotropic superconducting gap at the Brillouin zone centre of Tl0.63K0.37Fe1.78Se2

We performed a high-resolution angle-resolved photoemission spectroscopy study on superconducting (SC) Tl0.63K0.37Fe1.78Se2 (Tc = 29 K) in the whole Brillouin zone (BZ). In addition to a nearly isotropic ∼8.2 meV 2-dimensional (2D) SC gap (2Δ/kBTc ∼ 7) on quasi-2D electron Fermi surfaces (FSs) located around M(π,0,0)-A(π,0,π), we observe a ∼6.2 meV isotropic SC gap (2Δ/kBTc ∼ 5) on the Z-centred electron FS that rules out any d-wave pairing symmetry and rather favors an s-wave symmetry. All isotropic SC gap amplitudes can be fit by a single-gap function derived from a local strong-coupling approach suggesting an enhancement of the next-nearest neighbor exchange interaction in the ferrochalcogenide superconductors.

Dc Josephson current for d-wave superconductors with charge density waves

dc Josephson tunnel current Ic between a dx2−y2-wave superconductor and charge density waves (CDWs)—e.g. a high-Tc oxide and a conventional isotropic superconductor—was considered theoretically. Directionality of tunneling was taken into account. It was found that the dependence of Ic on the angle γ between the direction of the superconducting lobe and the plane normal to the junction is significantly altered by CDWs. For certain doping levels it may be nonmonotonic, as can be readily determined experimentally. For comparison, presented here are the corresponding results obtained for the tunnel junction between CDWs in an s-superconductor and a conventional isotropic superconductor.