Experimental evidence for vortex-glass superconductivity in Y-Ba-Cu-O

Evidence of second-order transition and critical scaling for the dynamical ordering transition in current-driven vortices

Dynamical ordering from a disordered plastic flow to an anisotropically ordered smectic flow induced by a dc force has been studied in various many-particle systems, including vortices in type-II superconductors. However, it remains unclear whether the dynamical ordering is a true phase transition because of lack of suitable experimental methods. Here, we study the response of vortex flow to the transverse force using a cross-shaped amorphous Mo[Formula: see text]Ge[Formula: see text] film. From transverse current-voltage (force-velocity) characteristics under various longitudinal currents, we find a change of the transverse response in low voltage (velocity) regions from a nonlinear to linear behavior at a well-defined longitudinal current that marks the dynamical ordering transition. We also find the scaling collapse of the transverse current-voltage curves to a universal scaling function, providing evidence of the second-order transition for the dynamical ordering transition.

Ordered Bose Glass of Vortices in Superconducting YBa2Cu3O7-δ Thin Films with a Periodic Pin Lattice Created by Focused Helium Ion Irradiation

The defect-rich morphology of YBa₂Cu₃O_7-δ (YBCO) thin films leads to a glass-like arrangement of Abrikosov vortices which causes the resistance to disappear in vanishing current densities. This vortex glass consists of entangled vortex lines and is identified by a characteristic scaling of the voltage-current isotherms. Randomly distributed columnar defects stratify the vortex lines and lead to a Bose glass. Here, we report on the observation of an ordered Bose glass in a YBCO thin film with a hexagonal array of columnar defects with 30 nm spacings. The periodic pinning landscape was engineered by a focused beam of 30 keV He⁺ ions in a helium-ion microscope.

Theory and experiments for disordered elastic manifolds, depinning, avalanches, and sandpiles

Domain walls in magnets, vortex lattices in superconductors, contact lines at depinning, and many other systems can be modeled as an elastic system subject to quenched disorder. The ensuing field theory possesses a well-controlled perturbative expansion around its upper critical dimension. Contrary to standard field theory, the renormalization group (RG) flow involves a function, the disorder correlator Δ(w), and is therefore termed the functional RG. Δ(w) is a physical observable, the auto-correlation function of the center of mass of the elastic manifold. In this review, we give a pedagogical introduction into its phenomenology and techniques. This allows us to treat both equilibrium (statics), and depinning (dynamics). Building on these techniques, avalanche observables are accessible: distributions of size, duration, and velocity, as well as the spatial and temporal shape. Various equivalences between disordered elastic manifolds, and sandpile models exist: an elastic string driven at a point and the Oslo model; disordered elastic manifolds and Manna sandpiles; charge density waves and Abelian sandpiles or loop-erased random walks. Each of the mappings between these systems requires specific techniques, which we develop, including modeling of discrete stochastic systems via coarse-grained stochastic equations of motion, super-symmetry techniques, and cellular automata. Stronger than quadratic nearest-neighbor interactions lead to directed percolation, and non-linear surface growth with additional Kardar-Parisi-Zhang (KPZ) terms. On the other hand, KPZ without disorder can be mapped back to disordered elastic manifolds, either on the directed polymer for its steady state, or a single particle for its decay. Other topics covered are the relation between functional RG and replica symmetry breaking, and random-field magnets. Emphasis is given to numerical and experimental tests of the theory.

Evidence for a vortex-glass transition in superconducting Ba(Fe0.9Co0.1)2As2

Measurements of magneto-resistivity and magnetic susceptibility were performed on single crystals of superconducting Ba(Fe0.9Co0.1)2As2 close to the conditions of optimal doping. The high quality of the investigated samples allows us to reveal dynamic scaling behaviour associated with a vortex-glass phase transition in the limit of a weak degree of quenched disorder. Accordingly, the dissipative component of the ac susceptibility is reproduced well within the framework of Havriliak-Negami relaxation, assuming a critical power-law divergence for the characteristic correlation time τ of the vortex dynamics. Remarkably, the random disorder introduced by the Fe1-xCox chemical substitution is found to act on the vortices as a much weaker quenched disorder than previously reported for cuprate superconductors such as Y1-xPrxBa2Cu3O7-δ.

Superconducting anisotropy in (CaCuO2)n/(SrTiO3)m superlattices

The superconducting properties of (CaCuO2)n/(SrTiO3)m artificial superlattices have been investigated via transport measurements under the application of external magnetic fields. The coherence lengths in the plane of the substrate and in the direction perpendicular to it (ξab and ξc, respectively) have been measured while varying m, the thickness of the SrTiO3 block. The results show that with increasing m, i.e. with increasing structural anisotropy, the superconducting anisotropy γ = ξab/ξc decreases. This apparent anomalous relation between the structural and the superconducting anisotropies suggests that γ is more affected by local doping at the interface rather than by the separation between the superconducting blocks. This interpretation of the experimental results has been confirmed by both the irreversibility lines and the magnetic field dependence of the activation energy for fluxon motion.

Voltage-current properties of superconducting amorphous tungsten nanostrips

The voltage-current (V-I) characteristics of tungsten (W) strips patterned by focused-ion-beam assisted deposition were studied at different temperatures and various magnetic fields applied perpendicular to the strips. At fields of 1 Tesla (T) and 2 T, a scaling behavior was observed in V-I isotherms, which can be fitted by quasi-three-dimensional (quasi-3D) vortex-glass (VG) to liquid transition theory.

Effects of discreteness on gauge glass models in two and three dimensions

The q-state clock gauge glass model is studied to see the effect of discreteness on the Kosterlitz-Thouless (KT) transition and the ferromagnetic (FM) critical phenomenon in random systems. The nonequilibrium relaxation analysis is applied. In two dimensions, the successive transitions of paramagnetic (PM), KT, and FM phases are investigated along the Nishimori line for q=6, 8, 10, 12, 14, 16, and 1024 (recognized as infinity) cases. For the upper critical temperature, it is found that the transition temperature is almost the same as in the continuous case for all q values. The lower transition temperature is found to be proportional to 1/q2. In three dimensions, the critical behavior of the PM-FM transition is studied along the Nishimori line for q=6, 8, 16, and 1024 cases. It is found that the spin discreteness is irrelevant, and the transition belongs to the same universality class as in the (continuous) XY case.

A new method to detect the vortex glass phase and its evidence in YBCO

The evidence of the vortex glass phase has been obtained by analysing the nonlinear magnetic response of type-II superconductors. The method introduced here is based on a combined frequency dependence analysis of the real and imaginary part of the 1st and 3rd harmonics of the AC magnetic susceptibility. The analysis has been performed by taking into account both the components and the Cole-Cole plots (i.e. the imaginary part as a function of the real part). Numerical simulations have been used to identify the fingerprints of the magnetic behaviour in the vortex glass phase. These characteristics allowed the vortex glass phase to be distinguished from the other disordered phases, even those showing similar electrical properties. Finally, this method has been successfully applied to detecting the vortex glass phase in an YBCO bulk melt-textured sample.

Effect of planar defects on the stability of the Bragg glass phase of type-II superconductors

It is shown that the Bragg glass phase can become unstable with respect to planar crystal defects as twin or grain boundaries. A single defect plane that is oriented parallel to the magnetic field as well as to one of the main axis of the Abrikosov flux line lattice is always relevant, whereas we argue that a plane with higher Miller index is irrelevant, even at large defect potentials. A finite density of parallel defects with random separations can be relevant even for larger Miller indices. Defects that are aligned with the applied field restore locally the flux density oscillations which decay algebraically with distance from the defect. The current-voltage relation is changed to lnV(J) approximately -J(-1). The theory exhibits striking similarities to the physics of Luttinger liquids with impurities.

Angular-dependent I-V characteristics in borocarbide superconductor YNi(2)B(2)C

We present angular-dependent current-voltage (I-V) measurements in borocarbide YNi(2)B(2)C single crystals near the vortex-glass irreversible line. External magnetic fields are applied along the angle θ with respect to the c-axis. The nonlinear I-V curves reveal scaling behaviour near the transition. Using the scaling analysis, the relevant critical exponents and vortex transition temperatures are determined for all orientations. The data agrees well with the vortex-glass (VG) model. No evidence was found that supports the existence of a Bose-glass (BG) type of transition.

Out-of-equilibrium dynamics of the vortex glass in superconductors

We study the relaxational dynamics of flux lines in high-temperature superconductors with random pinning using Langevin dynamics. At high temperatures the dynamics is stationary and the fluctuation dissipation theorem (FDT) holds. At low temperatures the system does not equilibrate with its thermal bath: a simple multiplicative aging is found, the FDT is violated, and we find that an effective temperature characterizes the slow modes of the system. The generic features of the evolution--scaling laws--are dictated by those of the single elastic line in a random environment.

Amorphous vortex glass phase in strongly disordered superconductors

We introduce a model describing vortices in strongly disordered three-dimensional superconductors. The model focuses on the topological defects, i.e., dislocation lines, in an elastic description of the vortex lattice. The model is studied using Monte Carlo simulations, revealing a glass phase at low temperatures, separated by a continuous phase transition to the high temperature resistive vortex liquid phase. The critical exponents nu approximately 1.3 and eta approximately -0.4 characterizing the transition are obtained from finite size scaling.

High current-carrying capability in c-axis-oriented superconducting MgB2 thin films

In high-quality c-axis-oriented MgB2 thin films, we observed high critical current densities ( J(c)) of approximately 16 MA/cm(2) at 15 K under self-fields comparable to those of cuprate high-temperature superconductors. The extrapolated value of J(c) at 5 K was estimated to be approximately 40 MA/cm(2). For a magnetic field of 5 T, a J(c) of approximately 0.1 MA/cm(2) was detected at 15 K, suggesting that this compound would be a very promising candidate for practical applications at high temperature and lower power consumption. The vortex-glass phase is considered to be a possible explanation for the observed high current-carrying capability.

Do superconductors have zero resistance in a magnetic field?

We show that dc voltage versus current measurements of a YBa(2)Cu(3)O(7-delta) film in a magnetic field can be collapsed onto scaling functions proposed by Fisher et al. [Phys. Rev. B 43, 130 (1991)] as is widely reported in the literature. We find, however, that good data collapse is achieved for a wide range of critical exponents and temperatures. These results strongly suggest that agreement with scaling alone does not prove the existence of a phase transition. We propose a criterion to determine if the data collapse is valid, and thus if a phase transition occurs. To our knowledge, none of the data reported in the literature meet our criterion.

Vortex glass transition and quantum vortex liquid at low temperature in a thick a- MoxSi1-x film

We present measurements of ac complex resistivity, as well as dc resistivity, for a thick amorphous MoxSi1-x film at low temperatures ( T>0.04 K) in various constant fields B. We find that the vortex glass transition (VGT) persists down to T approximately 0.04Tc0 up to B approximately 0.9Bc2(0), where Tc0 and Bc2(0) are the mean-field transition temperature and upper critical field at T = 0, respectively. In the limit T-->0, the VGT line Bg(T) extrapolates to a field below Bc2(0), while the dc resistivity rho(T) tends to the finite nonzero value in fields just above Bg(0). These results indicate the presence of a metallic quantum vortex liquid at T = 0 in the regime Bg(0)<B<Bc2(0).

Coulomb-Gas scaling law for a superconducting Bi(2+y)Sr(2-x-y)La(x)CuO(6+delta) thin films in magnetic fields

The electrical transport properties of epitaxial superconducting Bi(2+y)Sr(2-x-y)La(x)CuO(6+delta) thin films have been studied in magnetic fields. Using a modified Coulomb-gas scaling law, we can fit all the magnetic field dependent low resistance data with a universal scaling curve, which allows us to determine a relation between the activation energy of the thermally activated flux flow resistance and the characteristic temperature scaling parameters.

Phase diagram of a hard-sphere system in a quenched random potential: A numerical study

We report numerical results for the phase diagram in the density-disorder plane of a hard-sphere system in the presence of quenched, random, pinning disorder. Local minima of a discretized version of the Ramakrishnan-Yussouff free energy functional are located numerically and their relative stability is studied as a function of the density and the strength of disorder. Regions in the phase diagram corresponding to liquid, glassy, and nearly crystalline states are mapped out, and the nature of the transitions is determined. The liquid to glass transition changes from first to second order as the strength of the disorder is increased. For weak disorder, the system undergoes a first-order crystallization transition as the density is increased. Beyond a critical value of the disorder strength, this transition is replaced by a continuous glass transition. Our numerical results are compared with those of analytical work on the same system. Implications of our results for the field-temperature phase diagram of type-II superconductors are discussed.

Experimental evidence for the vortex glass phase in untwinned, proton irradiated YBa2Cu3O7-delta

We report on magnetoresistance measurements of the effects of 9 MeV proton irradiation on a clean, untwinned single crystal of YBa2Cu3O7-delta. For the first time, evidence for a vortex glass transition is detected in an untwinned single crystal of YBa2Cu3O7-delta with induced pointlike disorder, in which the first order vortex melting transition is completely suppressed after proton irradiation. Our results suggest that a sufficiently high pinning disorder is required in order for the vortex glass phase to be observed.

Dynamic phases and the peak effect in dirty type II superconductors

We study numerically and experimentally the dynamics of driven vortex matter. Our London-Langevin simulations find that the critical current exhibits a peak both across the Bragg glass to vortex glass transition and across the melting line. The peak is accompanied by a clear crossing of the I-V curves. We report transport measurements on untwinned YBCO crystals, in complete accordance with these findings. At higher drives disorder is averaged to reduced values, and in three dimensions the vortices reorder into a "moving solid." The effect of the disorder can be well represented with a "shaking temperature" which is inversely proportional to the velocity.