Vortex nanoliquid in high-temperature superconductors

Using a differential magneto-optical technique to visualize the flow of transport currents, we reveal a new delocalization line within the reversible vortex liquid region in the presence of a low density of columnar defects. This line separates a homogeneous vortex liquid, in which all the vortices are delocalized, from a heterogeneous "nanoliquid" phase, in which interconnected nanodroplets of vortex liquid are caged in the pores of a solid skeleton formed by vortices pinned on columnar defects. The nanoliquid phase displays high correlation along the columnar defects but no transverse critical current.     

Vortex washboard voltage noise in type-II superconductors

In order to characterize flux flow through disordered type-II superconductors, we investigate the effects of columnar and point defects on the vortex velocity/voltage power spectrum in the driven non-equilibrium steady state. We employ three-dimensional Metropolis Monte Carlo simulations to measure relevant physical observables including the force-velocity/current-voltage (I-V) characteristics, vortex spatial arrangement and structure factor, and mean flux line radius of gyration.Our simulation results compare well to earlier findings and physical intuition.We focus specifically on the voltage noise power spectra in conjunction with the vortex structure factor in the presence of weak columnar and point pinning centers. We investigate the vortex washboard noise peak and associated higher harmonics,and show that the intensity ratios of the washboard harmonics are determined bythe strength of the material defects rather than the type of pins present.Through varying columnar defect lengths and pinning strengths as well as magnetic flux density we further explore the effect of the material defects on vortex transport.It is demonstrated that the radius of gyration displays quantitatively uniquefeatures that depend characteristically on the type of material defects presentin the sample.     

Multiple changes of order of the vortex melting transition in Bi2Sr2CaCu2O8 with dilute columnar defects

A low concentration of columnar defects is reported to transform a first-order vortex lattice melting line in Bi2Sr2CaCu2O8 crystals into alternating segments of first- and second-order transitions separated by two critical points. As the density of columnar defects is increased, the critical points shift apart and the range of the intermediate second-order transition expands. The measurement of equilibrium magnetization and the mapping of the melting line down to 27 K was made possible by employment of the shaking technique.     

Effects of dilute columnar defects on the vortex matter in Bi2Sr2CaCu2O8+δ near the disorder-driven phase transition

Magneto-optical measurements are employed to characterize the disorder-driven vortex phase transition and the metastable disordered vortex state in heavy-ion irradiated and pristine regions of the same Bi₂Sr₂CaCu₂O_8+δ crystal. We find that dilute columnar defects, while hardly affect the disorder-driven phase transition line, significantly increase the lifetime of the metastable state created in the vicinity of this line. Study of flux injection from the pristine region into the irradiated region suggests that in presence of columnar defects a metastable disordered state may be created in the bulk, in addition to being injected from the edges.     

Anisotropic enhancement of superconductivity in heavy-ion irradiated (K,Ba)BiO3

We have measured the specific heat, resistivity, and ac susceptibility of (K,Ba)BiO3 single crystals before and after introduction of either point or columnar defects by electron (EI) or heavy-ion irradiation (HII). While the magnetic field dependence of these properties remains mainly unaffected by EI, the irreversibility line and the location of the specific heat anomaly are both shifted up in temperature after HII. The shift is apparent only if the magnetic field is applied parallel to the ion tracks. For perpendicularly applied fields, both lines lie at the same field as in the pristine sample. These experiments call the nature of the vortex liquid state into question.     

Dynamic and thermodynamic properties of porous vortex matter in Bi(2)Sr(2)CaCu(2)O(8) in an oblique magnetic field

Vortex matter in Bi(2)Sr(2)CaCu(2)O(8) with a low concentration of tilted columnar defects (CDs) was studied using magneto-optical measurements and molecular dynamics simulations. It is found that while the dynamic properties are significantly affected by tilting the magnetic field away from the CDs, the thermodynamic transitions are angle independent. The simulations indicate that vortex pancakes remain localized on the CDs even at large tilting angles. This preserves the vortex thermodynamics, while vortex pinning is considerably weakened due to kink sliding.     

Melting of "porous" vortex matter

Bitter decoration and magneto-optical studies reveal that in heavy-ion irradiated superconductors, a "porous" vortex matter is formed when vortices outnumber columnar defects. In this state ordered vortex crystallites are embedded in the "pores" of a rigid matrix of vortices pinned on columnar defects. The crystallites melt through a first-order transition while the matrix remains solid. The melting temperature increases with density of columnar defects and eventually turns into a continuous transition. At high temperatures a sharp kink in the melting line is found, signaling an abrupt change from crystallite melting to melting of the rigid matrix.     

Critical current densities and flux creep rate in Co-doped BaFe2As2 with columnar defects introduced by heavy-Ion irradiation

We report the formation of columnar defects in Co-doped BaFe₂As₂ single crystals with different heavy-ion irradiations. The formation of columnar defects by 200 MeV Au ion irradiation is confirmed by transmission electron microscopy and their density is about 40% of the irradiation dose. Magneto-optical imaging and bulk magnetization measurements reveal that the critical current density J_c is enhanced in the 200 MeV Au and 800 MeV Xe ion irradiated samples while J_c is unchanged in the 200 MeV Ni ion irradiated sample. We also find that vortex creep rates are strongly suppressed by the columnar defects. We compare the effect of heavy-ion irradiation into Co-doped BaFe₂As₂ and cuprate superconductors.     

Majorana modes at the ends of superconductor vortices in doped topological insulators

Recent experiments have observed bulk superconductivity in doped topological insulators. Here we ask whether vortex Majorana zero modes, previously predicted to occur when s-wave superconductivity is induced on the surface of topological insulators, survive in these doped systems with metallic normal states. Assuming inversion symmetry, we find that they do but only below a critical doping. The critical doping is tied to a topological phase transition of the vortex line, at which it supports gapless excitations along its length. The critical point depends only on the vortex orientation and a suitably defined SU(2) Berry phase of the normal state Fermi surface. By calculating this phase for available band structures we determine that superconducting p-doped Bi(2)Te(3), among others, supports vortex end Majorana modes. Surprisingly, superconductors derived from topologically trivial band structures can support Majorana modes too.     

Delocalization in two-dimensional disordered Bose systems and depinning transition in the vortex state in superconductors

We investigate a two-dimensional (2D) Bose system with the long range interactions in the presence of disorder. Formation of the bound states at strong impurity sites gives rise to a depletion of the superfluid density. We predict the intermediate superfluid state where the condensate and localized bosons are present simultaneously. We find that interactions suppress localization and that with the increase of the boson density the system experiences a sharp delocalization crossover into a state where all bosons are delocalized. We map our results onto a 3D system of vortices in type II superconductors in the presence of columnar defects; the intermediate superfluid state maps to an intermediate vortex liquid where vortex liquid neighbors pinned vortices. We predict the depinning crossover within the vortex liquid and depinning induced vortex lattice-Bose glass melting.     

Relaxation dynamics in type-II superconductors with point-like and correlated disorder

We employ an elastic line model to investigate the steady-state properties and non-equilibrium relaxation kinetics of magnetic vortex lines in disordered type-II superconductors using Langevin molecular dynamics (LMD). We extract the dependence of the mean vortex line velocity and gyration radius as well as the mean-square displacement in the steady state on the driving current, and measure the vortex density and height autocorrelations in the aging regime. We study samples with either randomly distributed point-like or columnar attractive pinning centers, which allows us to distinguish the complex relaxation features of interacting flux lines subject to extended vs. uncorrelated disorder. Additionally, we find that our new LMD findings match earlier Monte Carlo (MC) simulation data well, verifying that these two microscopically quite distinct simulation methods lead to macroscopically very similar results for non-equilibrium vortex matter.     

Nucleation and creep of vortices in superfluids and clean superconductors

The paper is devoted to vortex nucleation in uniform and nonuniform superflows in superfluids, and to creep of vortices trapped by twin boundaries and columnar defects in isotropic and anisotropic superconductors. The shape of a nuclated loop which yields the maximal nucleation rate is defined from the balance of the Lorentz and the line-tension forces. If the trapping energy is small, the contact angle at which the vortex line meets the plane of the twin-boundary or the axis of the columnar defect is also small. This may strongly enhance the rate of thermal nucleation and especially of quantum nucleation. In the analysis of quantum tunnelling it was assumed that the vortex has no mass and its motion is governed by the Magnus force, as expected for superfluids and very pure superconductors. Quantum nucleation rate from the traditional quasiclassical theory of macroscopic tunnelling is compared with the nucleation rate derived from the Gross-Pitaevskii theory of a weakly nonideal Bose-gas.     

Comparatively high in-field critical current in type-II superconductors from heterogeneous columnar pins: A molecular dynamics study

Theoretical work predicts that the strong dependence of T_c on pure shear strain within the a–b plane of optimally doped YBa₂Cu₃O_7?δ results in heterogenous columnar pins of vortex lines about dislocation lines and about nano-columns inclusions aligned in parallel to the c axis. The critical current of a rigid vortex lattice driven by the Lorentz force in the presence of such clusters of pin/antipin lines is computed using two-dimensional (2D) collective pinning theory and by numerical simulation of the corresponding 2D vortex dynamics. Both theory and computer calculation find that the antipin component of the heterogenous columnar pins contributes substantially to the net in-field critical current.     

Effect of vortex pinning by point defects on the lower critical field in layered superconductors

The lower critical field H _c1 in layered superconductors is calculated under the assumption that vortex pinning by point defects is strong in these materials. We consider the case of a purely electromagnetic coupling of vortex pancakes and the case of both the electromagnetic and Josephson couplings of the pancakes in a vortex line. In the latter case, singularities in the temperature dependence of H _c1 are predicted at certain characteristic temperatures.     

Generalized anisotropic scaling theory and the transverse meissner transition

We consider a depinning transition in vortex systems with columnar disorder and tilted applied magnetic fields. From scaling arguments and Monte Carlo simulations, we find that this transverse Meissner transition is governed by a fixed point which is anisotropic in all three directions. This generalization of conventional anisotropic scaling means that the correlation length in different directions diverges with different rates, and we derive exact results for the anisotropy exponents. We make predictions which can be tested in experiments on superconductors with columnar disorder.     

Vortex flow and transverse flux screening at the bose glass transition

We study the vortex phase diagram in untwinned YBCO crystals with columnar defects. These randomly distributed defects are expected to induce a "Bose glass" phase of localized vortices exhibiting a vanishing resistance and Meissner effect for magnetic fields H( perpendicular) transverse to the columns. We directly observe the transverse Meissner effect using a Hall probe array. As predicted, the Meissner state breaks down at temperatures T(s) that decrease linearly as H( perpendicular) increases. However, T(s) lies far below the conventional melting temperature T(m) determined by a vanishing resistivity, suggesting a regime where vortices are effectively localized even when rotated off the columnar defects.     

Scanning tunneling microscopy study of pinning-induced vortex lattice distortion in ion-irradiated NbSe2

We observe vortex pinning in 2.2 GeV Au-ion irradiated NbSe₂ by scanning tunneling microscopy (STM) at 3K. The ion irradiation generates columnar defects which act as pinning sites. At various external magnetic fields the vortex arrangement is clearly resolved but shows strong distortion. The location of individual defects is extracted from STM data and compared to the vortex arrangement.     

Asymmetric field profile in Bose glass phase of irradiated YBa2Cu3O(7-delta): loss of interlayer coherence around 1/3 of matching field

Magneto-optical imaging in YBa(2)Cu(3)O(7-delta) with tilted columnar defects (CD's) shows an asymmetric critical-state field profile. The observed hysteretic shift of the profile ridge (trough) from the center of the sample is explained by in-plane magnetization originating from vortex alignment along CD's. The extracted ratio of the in-plane to out-of-plane magnetization component has a maximum at 1/5 of matching field ( B(Phi)) and disappears above B(Phi)/3, suggesting a reduction of interlayer coherence well below B(Phi) in the Bose glass phase. Implications are discussed in comparison with the vortex liquid recoupling observed in irradiated Bi(2)Sr(2)CaCu(2)O(8+y).     

A possible role of amorphous regions at grain-boundary vertex points as linear defects on flux pinning in MgB2 films with columnar grain structure

We measured the transport properties of MgB₂ films having columnar grain structure with their axis normal to the substrate. When an external magnetic field was applied parallel to the grain axis, an enhanced critical current density has been observed, and this result has been ascribed to flux pinning induced by grain boundaries. The shape of the angular dependence of critical current density and its magnetic field dependence showed a quite similar resemblance to those of YBa₂Cu₃O_x films containing columnar defects, implying a possible existence of linear defects in MgB₂ films of columnar structure. We propose that the amorphous regions at the vertex points of three or more grain boundaries observed in microstructural studies correspond to the linear defects and these linear defects anchor the end points of the flux line dislocations of Frank-Read sources, by which the shear in the flux line lattice is actuated. This assumed mechanism is found to reasonably explain the magnetic field dependence of the flux pinning force density of MgB₂ films with columnar grain structure.