Search

The magnetic field of vortices in anisotropic superconducting films is considered in the framework of anisotropic London approach. It is found that at distances large relative to the core size, the magnetic field normal to the film surface may change sign. We find that the magnetic field attenuates at large distances as $1/r^3$ as it does in isotropic films, but the anisotropy induces an angular dependence to the supercurrents which causes the sign of the field to change for anisotropy parameters $\gamma=\lambda_2/\lambda_1>\sqrt{2}$ in some parts of the $(x,y)$ plane., Comment: 8 pages, 12 figures

The magnetic field of moving vortices in anisotropic superconductors is considered in the framework of time-dependent London approach. It is found that at distances large relative to the core size, the field may change sign that alludes to a non-trivial intervortex interaction which depends on the crystal anisotropy and on the speed and direction of motion. These effects are caused to the electric fields and corresponding normal currents which appear due to the moving vortex magnetic structure. We find that the motion related part of the magnetic field attenuates at large distances as $1/r^3$ unlike the exponential decay of the static vortex field. The electric field induced by the vortex motion decreases as $1/r^2$., Comment: 9 pages, 10 figures

The magnetic field hz of a moving Pearl vortex in a superconducting thin-film in (x,y) plane is studied with the help of the time-dependent London equation. It is found that for a vortex at the origin moving in +x direction, hz(x,y) is suppressed in front of the vortex, x&gt, 0, and enhanced behind (x&lt, 0). The distribution asymmetry is proportional to the velocity and to the conductivity of normal quasiparticles. The vortex self-energy and the interaction of two moving vortices are evaluated.

We take account of normal currents that emerge when vortices move. Moving Abrikosov vortices in the bulk and Pearl vortices in thin films are considered. Velocity dependent distributions of both normal and persistent currents are studied in the frame of time-dependent London equations. In thin films near the Pearl vortex core, these distributions are intriguing in particular., Comment: 8 pages,10 figures. arXiv admin note: text overlap with arXiv:2102.00073

We study the effects of anisotropic order parameters on the temperature dependence of London penetration depth anisotropy ${\ensuremath{\gamma}}_{\ensuremath{\lambda}}(T)$. After ${\mathrm{MgB}}_{2}$, this dependence is commonly attributed to distinct gaps on multiband Fermi surfaces in superconductors. We have found, however, that the anisotropy parameter may depend on temperature also in one-band materials with anisotropic order parameters $\mathrm{\ensuremath{\Delta}}(T,{\mathbit{k}}_{F})$; a few such examples are given. We have also found that for different order parameters, the temperature dependence of $\mathrm{\ensuremath{\Delta}}(T)/\mathrm{\ensuremath{\Delta}}(0)$ can be represented with good accuracy by the interpolation suggested by Einzel [J. Low Temp. Phys 131, 1 (2003)], which simplifies considerably the evaluation of ${\ensuremath{\gamma}}_{\ensuremath{\lambda}}(T)$. Of particular interest are mixed order parameters of two symmetries for which ${\ensuremath{\gamma}}_{\ensuremath{\lambda}}(T)$ may go through a maximum for a certain relative weight of two phases. Also, for this case we find that the ratio ${\mathrm{\ensuremath{\Delta}}}_{max}(0)/{T}_{c}$ may exceed substantially the weak-coupling limit of 1.76. It, however, does not imply strong coupling; rather, it is due to significantly anisotropic angular variation of $\mathrm{\ensuremath{\Delta}}$.

The anisotropic London equations taking into account the normal currents are derived and applied to the problem of the surface impedance in the Meissner state of anisotropic materials. It is shown that the complex susceptibility of the anisotropic slab depends on the orientation of the applied microwave field relative to the crystal axes. In particular, the anisotropic sample in the microwave field is subject to a torque, unless the field is directed along one of the crystal principle axes.

The magnetic response of $\mathrm{Ca}\mathrm{K}{({\mathrm{Fe}}_{0.949}{\mathrm{Ni}}_{0.051})}_{4}{\mathrm{As}}_{4}$ was investigated by means of the muon spin rotation/relaxation. The long-range commensurate magnetic order sets in below the N\'eel temperature ${T}_{\mathrm{N}}=50.0(5)$ K. The density-functional theory calculations have identified three possible muon stopping sites. The experimental data were found to be consistent with only one type of magnetic structure, namely, the long-range magnetic spin-vortex-crystal order with the hedgehog motif within the $ab$ plane and the antiferromagnetic stacking along the $c$ direction. The value of the ordered magnetic moment at $T\ensuremath{\approx}3$ K was estimated to be ${m}_{\mathrm{Fe}}=0.38(11){\ensuremath{\mu}}_{\mathrm{B}}$ (${\ensuremath{\mu}}_{\mathrm{B}}$ is the Bohr magneton). A microscopic coexistence of magnetic and superconducting phases accompanied by a reduction of the magnetic order parameter below the superconducting transition temperature ${T}_{\mathrm{c}}\ensuremath{\simeq}9$ K is observed. Comparison with 11, 122, and 1144 families of Fe-based pnictides points to existence of correlation between the reduction of the magnetic order parameter at $T\ensuremath{\rightarrow}0$ and the ratio of the transition temperatures ${T}_{\mathrm{c}}/{T}_{\mathrm{N}}$. Such correlations were found to be described by Machida's model for coexistence of itinerant spin-density-wave magnetism and superconductivity [K. Machida, J. Phys. Soc. Jpn. 50, 2195 (1981); S. L. Bud'ko et al., Phys. Rev. B 98, 144520 (2018)].

The self-energy of a moving vortex is shown to decrease with increasing velocity. The interaction energy of two parallel slowly moving vortices differs from the static case by a small term $\ensuremath{\propto}{v}^{2}$; the ``slow'' motion is defined as having the velocity $vl{v}_{c}={c}^{2}/4\ensuremath{\pi}\ensuremath{\sigma}\ensuremath{\lambda}$, where $\ensuremath{\sigma}(T)$ is the conductivity of normal excitations and $\ensuremath{\lambda}(T)$ is London penetration depth. For higher velocities, $vg{v}_{c}(T)$, the interaction energy of two vortices situated along the velocity direction is enhanced and in the perpendicular direction is suppressed compared to the static case.

A simple relation is established between the zero-$T$ penetration depth $\ensuremath{\lambda}(0)$ and the slope of ${\ensuremath{\lambda}}^{\ensuremath{-}2}(T)$ near ${T}_{c}$, similar to Helfand-Werthamer's relation for ${H}_{c2}(0)$ and the slope of ${H}_{c2}(T)$ at ${T}_{c}$ for the isotropic $s$-wave case with nonmagnetic scattering [E. Helfand and N. R. Werthamer, Phys. Rev. 147, 288 (1966)]. When the scattering parameter $\ensuremath{\rho}=\ensuremath{\hbar}v/2\ensuremath{\pi}{T}_{c}\ensuremath{\ell}$ ($v$ is the Fermi velocity and $\ensuremath{\ell}$ is the mean free path) varies from 1 to 10, the coefficient of proportionality between ${\ensuremath{\lambda}}^{\ensuremath{-}2}(0)$ and ${T}_{c}{(d{\ensuremath{\lambda}}^{\ensuremath{-}2}/dT)}_{{T}_{c}}$ changes from 0.43 to 0.38. Combining this relation with the Rutgers thermodynamic identity, one can express $\ensuremath{\lambda}(0)$ in terms of the slope ${(d{H}_{c2}/dT)}_{{T}_{c}}$ and the density of states.

We show on a few examples of one-band materials with spheroidal Fermi surfaces and anisotropic order parameters that anisotropies ${\ensuremath{\gamma}}_{H}$ of the upper critical field and ${\ensuremath{\gamma}}_{\ensuremath{\lambda}}$ of the London penetration depth depend on temperature, a feature commonly attributed to multiband superconductors. The parameters ${\ensuremath{\gamma}}_{H}$ and ${\ensuremath{\gamma}}_{\ensuremath{\lambda}}$ may have opposite temperature dependences or may change in the same direction depending on the Fermi-surface shape and on the character of the gap nodes. For two-band systems, the behavior of anisotropies is affected by the ratios of bands densities of states, Fermi velocities, anisotropies, and order parameters. We investigate in detail the conditions determining the directions of temperature dependences of the two anisotropy factors.

Strains in superconductors due to moving vortices and vortex lattices are discussed. It is shown that the energy stored in elastic strains increases with vortex velocity. For moving vortex lattices, the elastic energy depends on velocity orientation relative to the lattice having minimum for the velocity directed along one of the unit cell vectors of the moving lattice. It is shown that for supersonic motion, the vortex induced stress field has a shape similar to supersonic shock waves., Comment: 6 pages, 2 figures

We study vortex current distributions in narrow thin-film superconducting strips with the help of analytic expression of the vortex current derived within the London theory. Using definition of the...

Enhanced microwave absorption, larger than that in the normal state, is observed in fine grains of type-II superconductors (MgB2 and K3C60) for magnetic fields as small as a few % of the upper critical field. The effect is predicted by the theory of vortex motion in type-II superconductors, however its direct observation has been elusive due to skin-depth limitations; conventional microwave absorption studies employ larger samples where the microwave magnetic field exclusion significantly lowers the absorption. We show that the enhancement is observable in grains smaller than the penetration depth. A quantitative analysis on K3C60 in the framework of the Coffey–Clem (CC) theory explains well the temperature dependence of the microwave absorption and also allows to determine the vortex pinning force constant.

We use a scanning tunneling microscope to study the superconducting density of states and vortex lattice of single crystals of ${\mathrm{CaKFe}}_{4}{\mathrm{As}}_{4}$. This material has a critical temperature of ${T}_{c}=35$ K, one of the highest among stoichiometric iron based superconductors (FeBSCs), and is comparable to ${T}_{c}$ found near optimal doping in other FeBSCs. We observe quasiparticle scattering from defects with a pattern related to interband scattering between zone centered hole sheets. We measure the tunneling conductance in vortex cores and find a peak due to Caroli--de Gennes--Matricon bound states. The peak is located above the Fermi level, showing that ${\mathrm{CaKFe}}_{4}{\mathrm{As}}_{4}$ is a clean superconductor with vortex core bound states close to the so-called extreme quantum limit. We identify locations where the superconducting order parameter is strongly suppressed due to pair breaking. Vortices are pinned at these locations, and the length scale of the suppression of the order parameter is of order of the vortex core size. As a consequence, the vortex lattice is disordered up to 8 T.

Effective demagnetizing factors that connect the sample magnetic moment with the applied magnetic field are calculated numerically for perfectly diamagnetic samples of various non-ellipsoidal shapes. The procedure is based on calculating total magnetic moment by integrating the magnetic induction obtained from a full three dimensional solution of the Maxwell equations using adaptive mesh. The results are relevant for superconductors (and conductors in AC fields) when the London penetration depth (or the skin depth) is much smaller than the sample size. Simple but reasonably accurate approximate formulas are given for practical shapes including rectangular cuboids, finite cylinders in axial and transverse field as well as infinite rectangular and elliptical cross-section strips., updated version, corrected typos etc

We revisit the problem of the surface superconductivity nucleation focusing on the detailed study of the critical field $H_{c3}$ as a function of temperature and disorder. Using the semiclassical Eilenberger formalism we find that away from the Ginzburg-Landau region the ratio between the nucleation critical field $H_{c3}$ and the upper critical field $H_{c2}$ deviates strongly from the Saint-James-de Gennes limit. In particular, the $H_{c3}/H_{c2}$ is found to be a nonmonotonic function of temperature, which reaches the maximum for a set of parameters corresponding to a crossover region from ballistic to diffusive scattering, when the mean free path in a bulk of a superconductor is of the same order as zero-temperature superconducting coherence length. We also analyze the robustness of the nucleated phases with respect to diffusive scattering off the sample boundary by solving exactly corresponding eigenvalue problem of an integral equation for the critical field. The implications of these results for the transport in superconductors of various geometries near $H_{c3}$ are briefly discussed. In particular, we present results for the mechanism of magnetoconductivity oscillations due to surface superconductivity effects., 14 pages, 6 figures

It is of interest to determine the exit angle of a vortex from a superconducting surface, since this affects the intervortex interactions and their consequences. Two ways to determine this angle are to image the vortex magnetic fields above the surface, or the vortex core shape at the surface. In this work we evaluate the field h(x, y, z) above a flat superconducting surface x, y and the currents J(x,y) at that surface for a straight vortex tilted relative to the normal to the surface, for both the isotropic and anisotropic cases. In principle, these results can be used to determine the vortex exit tilt angle from analyses of magnetic field imaging or density of states data., Comment: 5 pages, 4 figures

It is shown that a vortex trapped in one of the banks of a planar edge-type Josephson junction in a narrow thin-film superconducting strip can change drastically the dependence of the junction critical current on the applied field, I c ( H ) . When the vortex is placed at certain discrete positions in the strip middle, the pattern I c ( H ) has zero at H = 0 instead of the traditional maximum of ‘0-type’ junctions. The number of these positions is equal to the number of vortices trapped at the same location. When the junction–vortex separation exceeds ∼ W , the strip width, I c ( H ) is no longer sensitive to the vortex presence. The same is true for any separation if the vortex approaches the strip edges.

In superconductors with strong coupling between superconductivity and elasticity manifested in a strong dependence of transition temperature on pressure, there is an additional contribution to inter-vortex interactions due to the strain field generated by vortices. When vortex lines are along the $c$ axis of a tetragonal crystal, a square vortex lattice (VL) is favored at low vortex densities, because the vortex-induced strains contribution to the inter-vortex interactions is long range. At intermediate magnetic fields, the triangular lattice is stabilized. The triangular lattice evolves to the square lattice upon increasing magnetic field, and eventually the system locks to the square structure. We argue, however, that as $B$ approaches $H_{c2}$ the elastic inter-vortex interactions disappear faster than the standard London interactions, so that VL should return to the triangular structure. Our results are compared to VLs observed in the heavy fermion superconductor $\mathrm{CeCoIn_5}$., 6 pages and 3 figures

A model of a clean two-band s-wave superconductor with cylindrical Fermi surfaces, different Fermi velocities v_{1,2}, and a general 2x2 coupling matrix V_{alpha beta} is used to study the order parameter distribution in vortex lattices. The Eilenberger weak coupling formalism is used to calculate numerically the spatial distributions of the pairing amplitudes Delta_1_ and Delta_2_ of the two bands for vortices parallel to the Fermi cylinders. For generic values of the interband coupling V_{12}, it is shown that, independently of the couplings V_{alpha beta}, of the ratio v_1 /v_2, of the temperature, and the applied field, the length scales of spatial variation of Delta_1 and of Delta_2 are the same within the accuracy of our calculations. The only exception from this single length-scale behavior is found for V_{12} --> 0, i.e., for nearly decoupled bands., 7 pages, 8 figures

A self-consistent two-gap &gamma, model is used to quantitatively describe several thermodynamic properties of MgB 2 superconductor. The superconducting coupling matrix, &nu, i j , was obtained from the fitting of the superfluid density in the entire superconducting temperature range. Using this input, temperature-dependent superconducting gaps, specific heat, and upper critical fields were calculated with no adjustable parameters and compared with the experimental data as well as with the first-principles calculations. The observed agreement between fit and data shows that &gamma, model provides adequate quantitative description of the two-gap superconductivity in MgB 2 and may serve as a relatively simple and versatile self-consistent description of the thermodynamic quantities in multi-gap superconductors.

Author(s): Taufour, V; Kaluarachchi, US; Kogan, VG | Abstract: We consider the phase diagram of a ferromagnetic system driven to a quantum phase transition with a tuning parameter p. Before being suppressed, the transition becomes of the first order at a tricritical point, from which wings emerge under application of the magnetic field H in the T-p-H phase diagram. We show that the edge of the wings merge with tangent slopes at the tricritical point.

We study the spatial distribution of the density of states (DOS) at zero bias N(r) in the mixed state of single and multigap superconductors. We provide an analytic expression for N(r) based on deGennes' relationship between DOS and the order parameter that reproduces well scanning tunneling microscopy (STM) data in several superconducting materials. In the single gap superconductor β-Bi2Pd, we find that N(r) is governed by a length scale ξH=φ0/2πH, which decreases in rising fields. The vortex core size C, defined via the slope of the order parameter at the vortex center, C (dΔ/dr|r→0)-1, differs from ξH by a material dependent numerical factor. The new data on the tunneling conductance and vortex lattice of the 2H-NbSe1.8S0.2 show the in-plane isotropic vortices, suggesting that substitutional scattering removes the in-plane anisotropy found in the two-gap superconductor 2H-NbSe2. We fit the tunneling conductance of 2H-NbSe1.8S0.2 to a two gap model and calculate the vortex core size C for each band. We find that C is field independent and has the same value for both bands. We also analyze the two-band superconductor 2H-NbS2 and find the same result. We conclude that, independently of the magnetic field induced variation of the order parameter values in both bands, the spatial variation of the order parameter close to the vortex core is the same for all bands, The work was supported by the Spanish Ministry of Economy and Competitiveness (FIS2014-54498-R, MAT2014-56143-R, MDM-2014-0377, and MDM2015-0538, Network of Excellence in Molecular Nanoscience MAT2014-52919-REDC), by the Comunidad de Madrid through program Nanofrontmag-CM (S2013/MIT- 2850), the Generalidad Valenciana through program Prometeo, and by EU (Cost MP-1201 and COST CA-15128). E.H. acknowledges support of COLCIENCIAS Programa Doctorados en el Exterior Convocatoria 568-2012 and S.M. of MECD: FPU14/04407. M.G. acknowledges the European Union Horizon 2020 Marie Curie Actions under the project SPIN2D (H2020/2014-659378). We acknowledge SEGAINVEX workshop of UAM and Banco Santander. The work of I.G. receives support from Axa Research Fund, FP7-PEOPLE-2013-CIG 618321 and the European Research Council (Grant No. 679080). Work of V.K. was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division. The Ames Laboratory is operated for the U.S. DOE by Iowa State University under Contract No. DE-AC02-07CH11358

We demonstrate a design for a scanning superconducting quantum interference device(SQUID) microscope in which the sample temperature can be varied over a large range. In this design, both sample and SQUID are in the same vacuum space, separated by a few microns. By firmly anchoring the SQUID to a low-temperature bath, the sample temperature can be changed while the SQUID remains superconducting. This allows magnetic imaging at varying sample temperatures with micron-scale spatial resolution and the sensitivity of a low- T c SQUID. We demonstrate this approach by imaging the temperature dependence of Abrikosov vortices in thin films of the high-temperature superconductor YBa 2 Cu 3 O 7−δ . We extract the in-plane penetration depth λ ab (T) in our samples from these measurements.

A two-band model with repulsive interband coupling and interband potential scattering is considered to elucidate their effects on material properties. In agreement with previous work, we find that the bands' order parameters ${\mathrm{\ensuremath{\Delta}}}_{1,2}$ differ, and the larger is at the band with a smaller normal density of states (DOS), ${N}_{n2}l{N}_{n1}$. However, the bands' energy gaps, as determined by the energy dependence of the DOS, are equal due to scattering. For each temperature, the gaps become zero at a certain critical interband scattering rate; i.e., for strong enough scattering the model material becomes gapless. In the gapless state, the DOS at band 2 is close to the normal state value, whereas at band 1 it has a V shape with nonzero minimum. When the normal bands DOS are mismatched, ${N}_{n1}\ensuremath{\ne}{N}_{n2}$, the critical temperature ${T}_{c}$ is suppressed even in the absence of interband scattering, ${T}_{c}({N}_{n1})$ has a domelike shape. With increasing interband scattering, the London penetration depth at low temperatures evolves from being exponentially flat to a power law and even to near linear behavior in the gapless state, the latter being easily misinterpreted as caused by order parameter nodes.

A two-band model with repulsive interband coupling and interband {\it transport} (potential) scattering is considered to elucidate their effects on material properties. In agreement with previous work, we find that the bands order parameters $\Delta_{1,2}$ differ and the large is at the band with a smaller normal density of states (DOS), $N_{n2}

The pressure dependence of the upper critical field, $H_\textrm{c2,c}$, of single crystalline FeSe was studied using measurements of the inter-plane resistivity, $\rho_{\textrm{c}}$ in magnetic fields parallel to tetragonal $c$-axis. $H_\textrm{c2,c}(T)$ curves obtained under hydrostatic pressures up to $1.56$ GPa, the range over which the superconducting transition temperature, $T_\textrm{c}$, of FeSe exhibits a non-monotonic dependence with local maximum at $p_1\approx$ 0.8 GPa and local minimum at $p_2\approx$ 1.2 GPa. The slope of the upper critical field at $T_\textrm{c}$, $\left(\textrm{d}H_\text{c2,c}/\textrm{d}T\right)_{T_\textrm{c}}$, also exhibits a non-monotonic pressure dependence with distinct changes at $p_1$ and $p_2$. For $pp_2$ the slope is in good quantitative agreement with a single band, orbital Helfand-Werthamer theory with Fermi velocities determined from Shubnikov-de Haas measurements. This finding indicates that Fermi surface changes are responsible for the local minimum of $T_\textrm{c}(p)$ at $p_2\approx$ 1.2 GPa., Comment: 5 pages, 4 figures

It is shown that the order parameter $\Delta$ induced in the normal part of superconductor-normal-superconductor proximity system is modulated in the magnetic field differently from vortices in bulk superconductors. Whereas $\Delta$ turns zero at vortex centers, the magnetic structure of these vortices differs from that of Abrikosov's., Comment: 5 pages, 7 figures

We describe the main ideas and some experimental outcomes of two experiments, both aimed to study quantum tunneling effects in high-T-C structures. In the first experiment, macroscopic quantum tunneling is demonstrated in grain boundary YBaCuO Josephson junctions revealing dissipation levels lower than expected and opening novel perspectives for quantum circuitry. In the second, the low temperature dissipation is dominated by quantum tunneling of individual Pearl vortices in ultra-thin CaBaCuO systems characterized by extremely long Pearl lengths. (c) 2006 Elsevier B.V. All rights reserved.

New thin-film Josephson junctions have recently been tested in which the current injected into one of the junction banks governs Josephson phenomena. One thus can continuously manage the phase distribution at the junction by changing the injected current. A method of calculating the distribution of injected currents is proposed for a half-infinite thin-film strip with source-sink points at arbitrary positions at the film edges. The strip width $W$ is assumed small relative to $\Lambda=2\lambda^2/d$, $\lambda$ is the bulk London penetration depth of the film material, $d$ is the film thickness., Comment: 5 pages, 7 figures

Data on macroscopic superconducting anisotropy of MgB$_2$ are reviewed. The data are described within a weak coupling two-gaps anisotropic s-wave model of superconductivity. The calculated ratio of the upper critical fields $\gamma_H=H_{c2,ab}/H_{c2,c}$ increases with decreasing temperature in agreement with available data, whereas the calculated ratio of London penetration depths $\gamma_{\lambda}=\lambda_c/\lambda_{ab}$ decreases to reach $\approx 1.1$ at T=0. Possible macroscopic consequences of $\gamma_{\lambda}\ne\gamma_H$ are discussed., Comment: accepted to Physica C, special MgB2 issue

We will briefly outline recent work done by the Ames Laboratory group and collaborators on synthesis and physical properties of newly discovered intermetallic superconductor, MgB2 (Tc≈40 K), produced in the form of sintered powder and wire segments with the emphasis to be on recent results that indicate that MgB2 may well have significant anisotropies associated with the superconducting state.

The upper critical field ${H}_{c2}$ and its anisotropy are calculated for order parameters with line nodes at the equators, ${k}_{z}=0$, of the Fermi surface of uniaxial superconductors. It is shown that characteristic features found in Fe-based materials (a nearly linear ${H}_{c2}(T)$ in a broad $T$ domain, a low and increasing on warming anisotropy ${\ensuremath{\gamma}}_{H}={H}_{c2,ab}/{H}_{c2,c}$) can be caused by competing effects of the equatorial nodes and of the Fermi surface anisotropy. For certain material parameters, ${\ensuremath{\gamma}}_{H}(T)\ensuremath{-}1$ may change sign upon warming, in agreement with the recorded behavior of FeTeS systems. It is also shown that the anisotropy of the penetration depth ${\ensuremath{\gamma}}_{\ensuremath{\lambda}}={\ensuremath{\lambda}}_{c}/{\ensuremath{\lambda}}_{ab}$ decreases upon warming to reach ${\ensuremath{\gamma}}_{H}$ at ${T}_{c}$, in agreement with data available. For some materials ${\ensuremath{\gamma}}_{\ensuremath{\lambda}}(T)$ may change upon warming, from ${\ensuremath{\gamma}}_{\ensuremath{\lambda}}g1$ at low $T\mathrm{s}$ to ${\ensuremath{\gamma}}_{\ensuremath{\lambda}}l1$ at high $T\mathrm{s}$.

The classical criterion for classification of superconductors as type I or type II based on the isotropic Ginzburg-Landau theory is generalized to arbitrary temperatures for materials with anisotropic Fermi surfaces and order parameters. We argue that the relevant quantity for this classification is the ratio of the upper and thermodynamic critical fields ${H}_{c2}/{H}_{c}$, rather than the traditional ratio of the penetration depth and the coherence length $\ensuremath{\lambda}/\ensuremath{\xi}$. Even in the isotropic case, ${H}_{c2}/{H}_{c}$ coincides with $\sqrt{2}\ensuremath{\lambda}/\ensuremath{\xi}$ only at the critical temperature ${T}_{c}$ and they differ as $T$ decreases, the long-known fact. Anisotropies of Fermi surfaces and order parameters may amplify this difference and render false the criterion based on the value of $\ensuremath{\kappa}=\ensuremath{\lambda}/\ensuremath{\xi}$.

We report measurements of electrical resistivity under pressure to $5.8$ GPa, magnetization to $6.7$ GPa, and ac susceptibility to $7.1$ GPa in $\mathrm{K}{\mathrm{Fe}}_{2}{\mathrm{As}}_{2}$. The previously reported change of slope in the pressure dependence of the superconducting transition temperature ${T}_{c}(p)$ at a pressure ${p}^{*}\ensuremath{\sim}1.8$ GPa is confirmed, and ${T}_{c}(p)$ is found to be nearly constant above ${p}^{*}$ up to $7.1$ GPa. The $T\text{\ensuremath{-}}p$ phase diagram is very sensitive to the pressure conditions as a consequence of the anisotropic uniaxial pressure dependence of ${T}_{c}$. Across ${p}^{*}$, a change in the behavior of the upper critical field is revealed through a scaling analysis of the slope of ${H}_{{c}_{2}}$ with the effective mass as determined from the $A$ coefficient of the ${T}^{2}$ term of the temperature-dependent resistivity. We show that this scaling provides a quantitative test for the changes of the superconducting gap structure and suggests the development of a ${k}_{z}$ modulation of the superconducting gap above ${p}^{*}$ as a most likely explanation.

Large high-quality single crystals of hole-doped iron-based superconductor (Ba1-xKx)Fe2As2 were grown over a broad composition range 0.22

We have investigated the temperature dependence of the H parallel to c flux line lattice structural phase transition from square to hexagonal symmetry, in the tetragonal superconductor LuNi2B2C ( T(c) = 16.6 K). At temperatures below 10 K the transition onset field, H2(T), is only weakly temperature dependent. Above 10 K, H2(T) rises sharply, bending away from the upper critical field. This contradicts theoretical predictions of H2(T) merging with the upper critical field and suggests that just below the H(c2)(T) curve the flux line lattice might be hexagonal.

The phase difference between the banks of an edge-type planar Josephson junction crossing the narrow thin-film strip depends on wether or not vortices are present in the junction banks. For a vortex close to the junction this effect has been seen by Golod, Rydh, and Krasnov, \prl {\bf 104}, 227003 (2010), who showed that the vortex may turn the junction into $\pi$-type. It is shown here that even if the vortex is far away from the junction, it still changes the 0-junction to $\pi$-junction when situated close to the strip edges. Within the approximation used, the latter effect is independent of the vortex-junction separation, a manifestation of topology of the vortex phase which extends to macroscopic distances of superconducting coherence., Comment: 4 pages, 3 figures

The reversible magnetization M(T,H) in high quality single crystals of Lu(Ni{sub 1-x}Co{sub x}){sub 2}B{sub 2}C with x=0-0.09 is measured in a broad T,H domain and interpreted within London theory corrected for nonlocality of the current -- vector-potential relation. Profound deviations in the data from the standard London result, M{proportional_to}ln(H{sub c2}/H) in intermediate fields H{sub c1}<

The transformation of the vortex lattice in a tetragonal superconductor which consists of the $45\ifmmode^\circ\else\textdegree\fi{}$ reorientation relative to the crystal axes is studied using the nonlocal London model. It is shown that the reorientation occurs as two successive second order (continuous) phase transitions. The transition magnetic fields are calculated for a range of parameters relevant for borocarbide superconductors in which the reorientation has been observed.

Josephson vortices at tricrystal boundaries with and without a {pi} junction in zero applied field are considered. It is shown that if the three tricrystal arms are conventional junctions, a one-flux-quantum {phi}{sub 0} vortex at or near the intersection has lower energy than one far from the intersection. If the largest Josephson length exceeds the sum of the other two, the tricrystal ceases to be a pinning site. If one of the tricrystal arms is a {pi} junction, a {phi}{sub 0}/2 vortex at the intersection is the ground state of the system, and an even number of {phi}{sub 0}/2 vortices is forbidden, whereas 3{phi}{sub 0}/2 and 5{phi}{sub 0}/2 correspond to possible but, in general, metastable states. For certain combinations of Josephson lengths, the 3{phi}{sub 0}/2 state has lower energy than the combined energy of the {phi}{sub 0}/2 vortex at the tricrystal joint and a {phi}{sub 0} vortex far from the joint. Conditions are discussed under which the 3{phi}{sub 0}/2 vortex can be observed. (c) 2000 The American Physical Society.

Pancake vortices in stacks of thin superconducting films or layers are considered. It is stressed that in the absence of Josephson coupling topological restrictions upon possible configurations of vortices are removed and various examples of structures forbidden in bulk superconductors are given. In particular, it is shown that vortices may skip surface layers in samples of less than a certain size R{sub c} which might be macroscopic. The Josephson coupling suppresses R{sub c} estimates. (c) 2000 The American Physical Society.

We investigated transport properties of ultra-thin CaBaCuO (CBCO) films, focusing on vortex dynamics. By measuring current-voltage characteristics we found evidence that at high temperatures the vortices are thermally activated at the edges of the bridge and pushed in, causing dissipation and power-law dependence of the voltage from the current. At lower temperatures, the experimental curves change shape. We compared these data with the predicted behaviour for vortex quantum tunnelling and found a very good agreement. Measurements performed at ultra-low temperatures (down to 60 mK) in a particular low noise environment provide additional evidence of the robustness of the observed effects. (c) 2007 Elsevier B.V. All rights reserved.

The reversible magnetization {ital M} of Lu(Ni{sub 1{minus}x}Co{sub x}){sub 2}B{sub 2}C with x=0 and 0.06 is measured in a broad temperature domain as a function of field orientation {theta} in the basal crystal plane. The data are interpreted within London theory extended for nonlocality of the current-field relation in superconductors. The dependence M({theta}) diminishes on warming, vanishes at T{sup {asterisk}}{lt}T{sub c}, and changes sign for T{gt}T{sup {asterisk}}. The low-T sign is opposite to what is expected from the known angular dependence of the upper critical field and therefore cannot be attributed to the latter. Upon doping with Co, the effect disappears with decreasing mean-free path in agreement with theory. {copyright} {ital 1999} {ital The American Physical Society}

The sin-Gordon equation for Josephson junctions with arbitrary misaligned anisotropic banks is derived. As an application, the problem of Josephson vortices at twin planes of a YBCO-like material is considered. It is shown that for an arbitrary orientation of these vortices relative to the crystal axes of the banks, the junctions should experience a mechanical torque which is evaluated. This torque and its angular dependence may, in principle, be measured in small fields, since the flux penetration into twinned crystals begins with nucleation of Josephson vortices at twin planes., Comment: 6 pages

We have studied, using small angle neutron scattering, the flux line lattice square to hexagonal symmetry transition in single crystal $\mathrm{Lu}({\mathrm{Ni}}_{1\ensuremath{-}x}{\mathrm{Co}}_{x}{)}_{2}{\mathrm{B}}_{2}\mathrm{C}$. Low Co concentrations $(xl0.1)$, which reduce the mean free path and increase the coherence length, also move the structural transition to higher fields than in the undoped system. These data, quantitatively understood within the framework of a theory that includes nonlocal corrections to the London model due to the Fermi surface anisotropy, can be modeled using a simple ratio of the nonlocality range to the intervortex spacing.

The flux line form factor in small angle neutron scattering and transport data determines the superconducting length scales and critical fields in single crystal ${\mathrm{ErNi}}_{2}{\mathrm{B}}_{2}\mathrm{C}$. For $H\ensuremath{\Vert}c$, the coherence length $\ensuremath{\xi}$ increases and the penetration depth $\ensuremath{\lambda}$ decreases when crossing ${T}_{N}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}6.0\mathrm{K}$, the N\'eel transition. The critical fields show corresponding anomalies near ${T}_{N}$. For $H\ensuremath{\perp}c$, the fourfold modulation of the upper critical field ${H}_{c2}$ is strongly temperature dependent, changing sign near ${T}_{N}$, and can be modeled using the anisotropy of the sublattice magnetization.

Single crystal samples of Lu(Ni{sub 1{minus}x}Co{sub x}){sub 2}B{sub 2}C have been prepared for x=0{endash}0.09. In-plane electrical resistivity measurements show that the residual resistivity of these samples increases linearly with {ital x}, though by less than is observed for polycrystalline samples. T{sub c} is suppressed by the cobalt substitution (from 16.0 K for x=0 to 9.5 K for x=0.09), though magnetization measurements indicate that this is not due to pair breaking by magnetic impurities. The critical field H{sub C2}(T) decreases with increasing Co concentration, and has some anisotropy between H{parallel}c and H{perpendicular}c. The ratio of the coherence length to the mean-free path ({xi}{sub 0}/l) is estimated, and found to be approaching the dirty limit ({xi}{sub 0}/l{gt}1) as {ital x} increases. These results are discussed with reference to nonlocal effects and the vortex lattice structure of the borocarbides in the mixed state. {copyright} {ital 1998} {ital The American Physical Society}

Nonlocal corrections to London equations are employed to describe a variety of vortex lattices seen through neutron scattering in cubic crystals of V{sub 3}Si with large {kappa} . Within this model the observed symmetries of vortex lattices and their coupling to the underlying crystal are reproduced. Predicted lattice structures are field dependent in agreement with the data. {copyright} {ital 1997} {ital The American Physical Society}

Nonlocal corrections to the London model are used to describe vortex lattices in ${\mathrm{LuNi}}_{2}$${\mathrm{B}}_{2}$C. Within this scheme in fields along the c axis, vortices should form a square lattice (rotated 45\ifmmode^\circ\else\textdegree\fi{} relative to the crystal axes afandfb) at large fields, should transform to a triangular one at a field ${\mathrm{H}}_{2}$, and to another triangular lattice at a still lower field ${\mathrm{H}}_{1}$. We argue that the transition at ${\mathrm{H}}_{2}$ is of second order, whereas at ${\mathrm{H}}_{1}$ it is of first order. In tilted fields, ${\mathrm{H}}_{2}$ is predicted to move to higher fields. Neutron-scattering data for ${\mathrm{ErNi}}_{2}$${\mathrm{B}}_{2}$C are discussed.