Vortex Glass State Research Articles

Flux pinning properties and microstructure of SmBa2Cu3Oy thin films with systematically controlled BaZrO3 nanorods

We report a way of tuning the flux pinning properties by controlling the size and number density of BaZrO3 (BZO) nanorods without much degradation of the superconducting properties. The BZO nanorods in REBa2Cu3Oy superconducting films are known as promising c-axis-correlated pinning centers. We fabricated SmBa2Cu3Oy (SmBCO) films with BZO nanorods by a low-temperature growth technique (LTG-SmBCO+BZO films). With decreasing substrate temperature of the upper layer Tsupper in LTG-SmBCO+BZO films, the diameter of BZO nanorods decreased and their number density increased, leading to a high matching field Bϕ. Also, the considerable upturn shifts in the irreversibility field line and plateau regions in the magnetic field dependence of critical current density Jc were observed in the range from Bϕ/3 to Bϕ. These results indicate that a Bose-glass-like state of vortices localized on BZO nanorods emerges, after overcoming the vortex glass state of vortices, which are frozen on inherent pointlike disorders within the films in this magnetic field range. With this technique, it is possible to tune the flux pinning properties.

Vortex glass state in superconductors with fractal clusters of normal phase

The influence of fractal clusters of a normal phase on the dynamics of vortices in a percolation superconductor is considered. It is established that a vortex glass state is formed in superconductors with a fractal cluster structure. The vortex glass phase can be identified by the initial part of its current-voltage characteristic. The dependence of the glassy exponent on the fractal dimension of normal phase cluster boundaries is found.

Ginzburg-Landau theory of type II superconductors in magnetic field

Thermodynamics of type II superconductors in electromagnetic field based on the Ginzburg-Landau theory is presented. The Abrikosov flux lattice solution is derived using an expansion in a parameter characterizing the ``distance'' to the superconductor-normal phase transition line. The expansion allows a systematic improvement of the solution. The phase diagram of the vortex matter in magnetic field is determined in detail. In the presence of significant thermal fluctuations on the mesoscopic scale (for example, in high ${T}_{c}$ materials) the vortex crystal melts into a vortex liquid. A quantitative theory of thermal fluctuations using the lowest Landau level approximation is given. It allows one to determine the melting line and discontinuities at melt, as well as important characteristics of the vortex liquid state. In the presence of quenched disorder (pinning) the vortex matter acquires certain ``glassy'' properties. The irreversibility line and static properties of the vortex glass state are studied using the ``replica'' method. Most of the analytical methods are introduced and presented in some detail. Various quantitative and qualitative features are compared to experiments in type II superconductors, although the use of a rather universal Ginzburg-Landau theory is not restricted to superconductivity and can be applied with certain adjustments to other physical systems, for example, rotating Bose-Einstein condensate.

Effect of Swelling on the Superconducting Characteristics in Electron-Doped β-ZrNCl and HfNCl

Layer-structured metal nitride chlorides M NCl ( M =Zr, Hf) were electron-doped by the intercalation of alkali metals ( A =Li and Na) to form A x M NCl, and then swelled with organic solvent molecules [tetrahydrofuran (THF) and propylene carbonate (PC)]. Upon swelling, the organic molecules were cointercalated with the alkali metals, resulting in the basal spacing of A x M NCl being expanded by 5.6–18.5 Å and the superconducting transition temperatures ( T c s) increasing by ∼2 K. When the magnetization data were plotted as a function of temperature, an irreversibility temperature ( T irr ) was observed, where the zero-field-cooled (ZFC) and field-cooled (FC) magnetization superimpose. The reversible temperature range ( T c - T irr ) was markedly increased upon swelling. The slope of the plot of log H (applied magnetic field) vs log (1- T irr / T c ) was increased for the swelled system. The slope n in the power-law relationship for Na 0.28 (PC) y HfNCl and Li 0.5 (THF) y HfNCl is obtained to be n = 4.8–5.4. This finding implies a significant weakening of vortex pinning in the swelled phase. To investigate the irreversibility microscopically, nuclear magnetic resonance (NMR) measurements were carried out on Li 0.5 (THF) y HfNCl. The 1 H- and 7 Li-NMR relaxation and chemical shift suggested the relevance of vortex motions to the depinning at T irr , which is the depinning temperature between the thermally excited pancake vortex liquid state at higher temperatures and the pancake vortex glass state at lower temperatures.

Magnetic-field-induced phase transition of vortex glass states in disordered Josephson junction arrays

Using the resistively shunted junction model，we study magnetic-field-induced phase transitions of the vortex glass states in a disordered two-dimensional Josephson junction array. From calculated results of the vorticity of the vortex system and the voltage noise generated by current-driven vortices as a function of the magnetic field， the following conclusions can be drawn. 1） With decreasing the magnetic field， the vortex system exhibits a reentrant transition from a vortex glass phase to a pinned dilute vortex liquid. 2） There is a peak of voltage noise driven by the current in the vortex glass state. It follows that the system is in a sub-stable state as a result of the competition between ordered and disordered interactions， which results in peak effects of the critical current. The calculated results are consistent with recent experimental reports by Okuma and Kamada on disordered and superconducting MoxSi1-x films.

Synchronization in stacked array of the Josephson junctions in Bi 2Sr 2CaCu 2O 8+δ

Intrinsic stacked array of Josephson junctions will find potential application as voltage standard or HTSC Josephson spectral detector if internal Josephson oscillations in different layers can be synchronized under electromagnetic radiation. In our experiments we studied synchronization is stacked array of Josephson oscillations contained up to 2500 junctions in Bi 2Sr 2CaCu 2O 8+δ. Phase locking of the internal Josephson oscillation in array to externally applied microwave radiation was manifested by observation of the collective Shapiro steps. Synchronization of all junctions in array was possible in the vortex glass state in high magnetic fields and vortex liquid state on the B– T c-axis vortex phase diagram in frequency range 80–140 GHz. In those regions damping is significantly enhanced and hysteresis on I– V characteristics collapsed. Observations deny major opinion that intrinsic Josephson junctions in Bi 2Sr 2CaCu 2O 8+δ are always underdamped. We interpret our results as a reflecting the pancake vortex disorder and fluctuations in CuO 2 layers.

C-axis correlated pinning behavior near the irreversibility fields

The authors found that the peak at the parallel external field (B‖c) to the c axis in the angular dependence of Jc shrinks and almost disappears with increasing a magnetic field but it grows again with further increasing of a magnetic field at various temperatures for high-Jc Sm1+xBa2−xCu3Oy films. These behaviors can be explained by the flux pinning properties of the interstitial vortices, which locate in between the vortices pinned by the c-axis correlated disorders. From the obtained experimental results, the collective correlated pinned glass state is proposed in a high field region in the vortex glass states.

Hierarchical Nature of the Vortex Matter in Type II Superconductors due to Competition Between Interactions, Thermal Fluctuations and Disorder

We describe quantitatively the combined effects of both the thermal fluctuations and of the quenched disorder via the replica trick applied to the Ginzburg–Landau (GL) theory. We show that the vortex state can appear in either of the three disordered phases: (i) unpinned vortex liquid, (ii) amorphous vortex glass (pinned), and (iii) the crystalline (pinned but not containing topological defects) Bragg glass. The formation of the vortex glass is associated with the continuous replica symmetry breaking (RSB) reflecting the hierarchial structure of the potential barriers in a vortex glass state. An earlier analysis in the framework of London approximation have established that activation barriers controlling vortex dynamics obey the extreme value statistics within roughly the same domain of the phase diagram. We show that the disordered GL model in which only the coefficient at the quadratic term |ψ |2 is random, first considered by Dorsey et al., exhibits, in the gaussian approximation, an additional non-hierarchical state possessing certain glassy properties like nonzero Edwards–Anderson order parameter. We associate this state with the “marginal glass phase” predicted in the earlier work of one of the authors; the marginal glass state being characterized by the marginally glassy dynamics. We show further that when the random component of the coefficient of the quartic term |ψ |4 in GL free energy is taken into account, RSB effects appear. Application of the obtained results to description of various disorder-generated phenomena in vortex matter are briefly considered. The location of the glass transition line is determined and compared to experiments. This line is clearly different from both the melting line and the second peak line describing the translational and rotational symmetry breaking at high and low temperatures respectively. The phase diagram is separated by these two lines into the four phases described above.

Muons as Local Probes of Three-Body Correlations in the Mixed State of Type-II Superconductors

The vortex glass state formed by magnetic flux lines in a type-II superconductor is shown to possess nontrivial three-body correlations. While such correlations are usually difficult to measure in glassy systems, the magnetic fields associated with the flux vortices allow us to probe these via muon-spin rotation measurements of the local field distribution. We show via numerical simulations and analytic calculations that these observations provide detailed microscopic insight into the local order of the vortex glass and more generally validate a theoretical framework for correlations in glassy systems.

On the response of an oscillatory medium to defect generation

We investigate the response of a system far from equilibrium close to an oscillatory instability to the induction of phase singularities. We base our investigation on a numerical treatment of the complex Ginzburg-Landau equation (CGLE) in two spatial dimensions, which is considered as an order-parameter equation for lasers and other nonlinear optical systems. Defects are randomly generated by a spatially modulated linear growth rate. In the amplitude-turbulent regime, no qualitative change of behaviour can be detected. Phase-turbulent patterns emerging due to the Benjamin-Feir instability are destroyed by the externally injected defects. One observes either states consisting of spiral structures of various sizes which resemble the vortex glass states of the unperturbed system or a travelling wave pattern containing moving topological defects. In parameter space, both states are separated by a well-defined phase boundary which is close to the line separating convectively from absolutely stable travelling waves.

Doping dependence of the vortex glass and sublimation transitions in the high-Tc superconductor La2-xSrxCuO4 as determined from macroscopic measurements

Magnetization and ac-susceptibility measurements are used to characterize the mixed phase of the high-temperature cuprate superconductor La2-xSrxCuO4 over a large range of doping (0.075 $\leq~x\leq$ 0.20). The first order vortex lattice phase transition line HFOT(T), the upper critical field Hc2(T) and the second peak Hsp(T) have been investigated up to high magnetic fields (8 Tesla applied perpendicular to the CuO2 planes). Our results reveal a strong doping dependence of the magnetic phase diagram, which can mainly be explained by the increasing anisotropy with underdoping. Within our interpretation, the first order vortex lattice phase transition is due to the sublimation (rather than melting) of the vortex lattice into a gas of pancake vortices, whereas the second peak is related to the transition to a more disordered vortex glass state.

Magnetic flux penetration into superconductor in vortex-liquid and vortex-glass regimes

Magnetic flux penetration into a half-space occupied by a type-II superconductor occurring in a vor- tex-liquid or vortex-glass state is considered under the assumption that magnetic field exhibits a sharp increase with time (in the blow-up regime) at the interface. It is shown that each phase admits effective localization of magnetic flux in the form of a magnetic wave front, which is stopped at a depth of x s ∝ e - σ σ in a vortex-liquid regime and at x s ∝ (2 σ ) 1/( σ + 2) in a vortex-glass regime. Here, the parameter σ = U 0 / T depends on the thermal activation barrier height U 0 and on the temperature T in the vicinity of the melting curve T m ( B ) at a given mag- netic field induction B. © 2005 Pleiades Publishing, Inc.

The elusive Bose metal.

The conventional theory of metals is in crisis. In the past 15 years, there has been an unexpected sprouting of metallic states in low-dimensional systems, directly contradicting conventional wisdom. For example, bosons are thought to exist in one of two ground states: condensed in a superconductor or localized in an insulator. However, several experiments on thin metal-alloy films have observed that a metallic phase disrupts the direct transition between the superconductor and the insulator. We analyze the experiments on the insulator-superconductor transition and argue that the intervening metallic phase is bosonic. All relevant theoretical proposals for the Bose metal are discussed, particularly the recent idea that the metallic phase is glassy. The implications for the putative vortex-glass state in the copper oxide superconductors are examined.

Vortex-melting and vortex-glass transitions in a high purity twinnedYBa2Cu3O7−δsingle crystal

We present experimental evidence for the coexistence of a first-order vortex-lattice melting transition and a continuous vortex-glass melting transition at a lower temperature in high purity twinned ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ single crystal samples grown in ${\mathrm{BaZrO}}_{3}$ crucibles. The correlation of temperature T and magnetic field H dependence of the electrical resistivity $\ensuremath{\rho}$ and electric field vs current density E vs J isotherms is consistent with a two-step phase transition from the normal to the superconducting state. Analysis of the data strongly indicates that the vortex matter in the single crystal is inhomogeneous. This scenario is supported by the observation of a vortex-lattice melting at a temperature separating two vortex-glass states with different critical exponents $\ensuremath{\nu}(z\ensuremath{-}1).$ In light of independently performed numerical simulations [Crabtree et al., Phys. Rev. B 61, 1446 (2000)], the data support a scenario where the intermediate phase crosses over from a state where vortex lines in the twin boundaries are pinned and those within the bulk undergo driven plastic vortex flow, to a state where the vortex lines in and near the twin boundaries undergo driven disordered motion and those within the bulk move as an ordered lattice.

A theory of the thermal depinning transition in type-2 superconductors

Abstract It is pointed out theoretically that the electric field, E , vs. current density, J , characteristic of the vortex glass state is different from that predicted by M.P.A. Fisher; that is, the electric resistivity, ρ = E / J has a finite value even at J →0, while the Fisher theory predicts ρ →0 with J →0. It is also pointed out that the vortex glass–liquid transition is merely a kind of the bifurcation transition in the mixed state of type-2 superconductors containing pinning centers, which may be called the thermal depinning transition between the pinning state and the depinning state of fluxoids resulting from the thermal agitation on fluxoids. Furthermore, it is shown theoretically that only the flux flow resistivity obeys the scaling law near the thermal depinning transition temperature, T dp , while the flux creep resistivity approaches a finite value as J is decreased to zero, even in the pinning state below T dp . When ρ is measured down to a very small level of E , therefore, the noticeable deviation from the scaling law of ρ against J that was predicted by Fisher is expected to appear due to the above-mentioned behavior of the flux creep resistivity. The above theoretical conclusion that is contrary to the theoretical prediction by Fisher, however, seems to be supported by the recently observed data over a very wide range of the electric field, E provided by Kodama et al., because the present theoretical expression for the E vs. J , characteristics agrees quantitatively with these observed data.

Slow relaxation of low-temperature vortex phases inBi2Sr2CaCu2O8

Nonlinear transport in the low temperature vortex glass state of single crystal Bi_{2}Sr_{2}CaCu_{2}O_{8} has been investigated over long times (up to two weeks) with fast current pulses driven along the ab plane. It is found that at low temperature and high magnetic field both zero field cooled (ZFC) and field cooled (FC) samples relax towards the same equilibrium state, which is much closer to the original ZFC state than to the FC state. The implication of this FC metastability for the vortex phase diagram is discussed in the context of previous measurements.

Vortex phase diagram of a weakly pinned YBa2Cu3O7−δ crystal for H || c

The vortex phase diagram in a weakly pinned crystal of YBa2Cu3O7−δ (YBCO) for H || c is reviewed in the light of a recent elucidation of the process of ‘inverse melting’ in a bismuth cuprate system and the imaging of an interface between the ordered and the disordered regions across the peak effect in 2H-NbSe2. In the given YBCO crystal, a clear distinction can be made between the second magnetization peak and the peak effect in between 65 K and 75 K. The field region between the peak fields of the second magnetization peak (Hmsmp) and the onset fields of the peak effect (Honpe) is not only continuously connected to the Bragg glass phase at lower fields, but it is also sandwiched between the higher temperature vortex liquid phase and the lower temperature vortex glass phase. Thus, an ordered vortex state between (Hmsmp) and (Honpe) can get transformed to the (disordered) vortex liquid state on heating as well as to the (disordered) vortex glass state on cooling, a situation analogous to the thermal melting and the inverse melting phenomenon seen in a bismuth cuprate.

Phase-coherence threshold and vortex-glass state in diluted Josephson-junction arrays in a magnetic field

We study numerically the interplay of phase coherence and vortex-glass state in two-dimensional Josephson-junction arrays with average rational values of flux quantum per plaquette $f$ and random dilution of junctions. For $f=1/2$, we find evidence of a phase coherence threshold value $x_s$, below the percolation concentration of diluted junctions $x_p$, where the superconducting transition vanishes. For $x_s < x < x_p$ the array behaves as a zero-temperature vortex glass with nonzero linear resistance at finite temperatures. The zero-temperature critical currents are insensitive to variations in $f$ in the vortex glass region while they are strongly $f$ dependent in the phase coherent region.

I– V Characteristics of Bi 2Sr 2CaCu 2O 2+ δ single crystals in magnetic fields

Current–voltage ( I– V) measurements on mesa-structured Bi 2Sr 2CaCu 2O 8+ δ single crystals have been performed to study the interlayer coupling between Cu–O superconducting layers and vortex states in presence of the Josephson current and magnetic fields along the c-axis. At lower temperatures than 25 K, a pronounced effect of magnetic fields to the I– V characteristics appears in multiple-branching behaviour, when magnetic fields exceed the dimensional-crossover field B 2D. This is considered as a consequence of missing a long-range order of correlation of the vortex lines along the c-axis, reflecting the transition to vortex glass state from vortex lattice state. At higher temperatures, the effect is observed in an abrupt change of the Josephson critical current at magnetic fields lower than the B 2D and the melting field B m. This might be a possible evidence of the reduction in the magnetic fields of the peak effect and the melting transition in presence of the Josephson current.

Metastability line in the phase diagram of vortices inBi2Sr2CaCu2O8

Nonlinear transport in the low-temperature vortex glass state of single crystal ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8}$ has been investigated with fast current pulses driven along the $\mathrm{ab}$ plane. Field cooled preparation shows a higher threshold current (marking a jump or break in slope in the voltage response) than the zero field cooled (ZFC) one, but it is found to be metastable and convertible to the ZFC response by a small field excursion. The metastability appears on the low temperature side of the peak in the temperature dependence of the ZFC threshold current. It is suggested that the onset of metastability signals a different thermodynamic ground state.