Vortex-glass Transition Research Articles

Effects of self field and low magnetic fields on the normal-superconducting phase transition

Researchers have studied the normal-superconducting phase transition in the high-$T_c$ cuprates in a magnetic field (the vortex-glass or Bose-glass transition) and in zero field. Often, transport measurements in "zero field" are taken in the Earth's ambient field or in the remnant field of a magnet. We show that fields as small as the Earth's field will alter the shape of the current vs. voltage curves and will result in inaccurate values for the critical temperature $T_c$ and the critical exponents $\nu$ and $z$, and can even destroy the phase transition. This indicates that without proper screening of the magnetic field it is impossible to determine the true zero-field critical parameters, making correct scaling and other data analysis impossible. We also show, theoretically and experimentally, that the self-field generated by the current flowing in the sample has no effect on the current vs. voltage isotherms.

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.

Scaling of the B-dependent resistivity for different orientations in Fe doped YBa 2Cu 3O 7− δ

The angular dependence of a previously proposed modified model of the vortex glass transition has been investigated. The in-plane resistivity in an optimally oxygen doped YBa 2Cu 3O 7− δ single crystal, doped with 1% Fe, was measured in fields up to 12 T applied with different orientations with respect to the crystallographic c-axis. The transition curves at all orientations were successfully scaled into one curve according to a scaling variable for the normalized resistivity. Characteristic parameters of the model, like the glass transition temperature and the magnetic field B 0, were measured at each orientation and were in good agreement with the expected values. These results show that the model proposed is valid also for fields applied outside the c-axis, giving further support to a more consistent description of the vortex liquid resistivity.

Vortex-glass transitions in low-Tcsuperconducting Nb thin films andNb∕Cusuperlattices

Nb/Cu superconducting superlattices have been fabricated by dc magnetron sputtering. This system shows a vortex glass transition with critical exponents similar to high temperatures superconductors exponents. The transition dymensionality is governed by the superconducting coupling regime. The vortex glass transition shows a pure two dimensional behavior in decoupled superlattices and a quasi-two dimensional behavior in the superlattice coupling regime.

Vortex pinning by a columnar defect in planar superconductors with point disorder

We study the effect of a single columnar pin on a $(1+1)$ dimensional array of vortex lines in planar type II superconductors in the presence of point disorder. In large samples, the pinning is most effective right at the temperature of the vortex glass transition. In particular, there is a pronounced maximum in the number of vortices which are prevented from tilting by the columnar defect in a weak transverse magnetic field. Using renormalization group techniques we show that the columnar pin is irrelevant at long length scales both above and below the transition, but due to very different mechanisms. This behavior differs from the disorder-free case, where the pin is relevant in the low temperature phase. Solutions of the renormalization equations in the different regimes allow a discussion of the crossover between the pure and disordered cases. We also compute density oscillations around the columnar pin and the response of these oscillations to a weak transverse magnetic field.

Normal-superconducting phase transition mimicked by current noise

As a superconductor goes from the normal state into the superconducting state, the voltage versus current characteristics at low currents change from linear to nonlinear. We show theoretically and experimentally that the addition of current noise to nonlinear voltage versus current curves will create ohmic behavior. Ohmic response at low currents for temperatures below the critical temperature ${T}_{c}$ mimics the phase transition and leads to incorrect values for ${T}_{c}$ and the critical exponents $\ensuremath{\nu}$ and $z$. The ohmic response occurs at low currents, and will occur in both the zero-field transition and the vortex-glass transition. Our results indicate that the transition temperature and critical exponents extracted from the conventional scaling analysis are inaccurate if current noise is not filtered out. This is a possible explanation for the wide range of critical exponents found in the literature.

Vortex dynamics and possible vortex states just below the vortex-glass phase

We have measured current-induced voltage noise ${S}_{V}$ of thick amorphous ${\mathrm{Mo}}_{x}{\mathrm{Si}}_{1\ensuremath{-}x}$ films in various fields $H$ from zero to high fields near the vortex-glass (VG) transition ${H}_{g}$. Irrespective of temperature $T$, ${S}_{V}$ is highest in the Meissner phase $(Hl{H}_{c1})$. With applying $H$ that exceeds ${H}_{c1}$, ${S}_{V}$ decreases abruptly and falls to the background level. With further increasing $H$, ${S}_{V}$ then starts to rise at characteristic field ${H}_{Lg}^{0}(⪡{H}_{g})$ and the broad peak resulting from a plastic-flow motion of VG occurs before ${H}_{g}$ is approached. Combined with the ${S}_{V}$ data for the Corbino disk, we suggest that the edge-contamination effects reported in the clean ${\mathrm{NbSe}}_{2}$ single crystals are not important in our disordered films. Within the $T$ range studied, ${H}_{Lg}^{0}(T)$ shows an increase on cooling, which is different from the $T$-independent disorder-driven transition. We interpret the field regime ${H}_{c1}(T)lH(T)l{H}_{Lg}^{0}(T)$ as the vortex state different from the VG phase.

Critical dynamics of vortices near the second-order transition and quantum fluctuations

We measure the ac complex resistivity in the mixed state of amorphous Mo x Si 1− x films with different thicknesses ( t). For films with t=100 and 30 nm we can determine the vortex-glass-transition (VGT) line which persists down to low temperatures ( T) up to high fields ( B) near the upper critical field at T=0. In the liquid phase the vortex-relaxation time ( τ g) extracted from the frequency dependence of ac resistivity follows the power-law T dependence expected by the VG theory for three dimensions (3D). For the thinner (10, 6 nm) films, both the dc resistivity and τ g follow the activated T dependence except for the very low- T region, suggestive of 2D VGT. For all of the films studied, τ g in high B shows a decreased T dependence at lower T, indicating the quantum-driven fluctuations.

Zero-field superconducting phase transition obscured by finite-size effects in thickYBa2Cu3O7−δfilms

We report on the normal-superconducting phase transition in thick $\mathrm{YBa_{2}Cu_{3}O_{7-\delta}}$ films in zero magnetic field. We find significant finite-size effects at low currents even in our thickest films ($d = 3200$ \AA). Using data at higher currents, we can unambiguously find $T_c$ and $z$, and show $z = 2.1 \pm 0.15$, as expected for the three-dimensional XY model with diffusive dynamics. The crossover to two-dimensional behavior, seen by other researchers in thinner films ($d \leq 500$ \AA), obscures the three-dimensional transition in both zero field and the vortex-glass transition in field, leading to incorrect values of $T_c$ (or $T_g$), $\nu$, and $z$. The finite-size effects, usually ignored in thick films, are an explanation for the wide range of critical exponents found in the literature.

Jump in c-axis transport at the Bragg glass–vortex glass transition

We present dynamical simulations of anisotropic three-dimensional superconductors with point disorder. We study the three-dimensional XY model with anisotropy and the external magnetic field along the c-axis. This model has been shown to have a first-order transition as a function of the intensity of point disorder. We add an external current drive to the model and include both supercurrents and dissipative currents in the dynamics. We obtain current–voltage curves as a function of disorder at finite temperatures with current applied along the c-axis. We will show how the nonlinear current–voltage curves change as a function of disorder intensity across the transition line. The first-order character of the transition shows up clearly as a jump in the nonlinear transport response along the c-axis.

Vortex glass transition in a YBa 2Cu 3O 7− δ film with patterned pinning geometry

We report on multiterminal transport measurement in YBa 2Cu 3O y films, where a vortex flow channel is artificially introduced in a strong pinning environment with columnar defects. The samples were prepared by partially masked heavy-ion irradiation. Two kinds of phase transitions with different transition temperatures, T VG and T BG, which correspond to the vortex glass transition and the Bose glass transition, are observed for the unirradiated region and the irradiated one, respectively. At high field, the situation of T VG< T BG, where the flux flow in unirradiated channel is confined between Bose glass solids of the irradiated region, is realized. The vortex velocity distribution is almost homogeneous inside the channel. Around the boundary, however, we find that the vortices flowing in the unirradiated channel drag the vortices of the Bose glass solid in the irradiated region.

Suppression of the vortex glass transition due to correlated defects with a persistent direction perpendicular to an applied magnetic field

It is found on the basis of the lowest Landau level approach for the Ginzburg-Landau model that, in bulk type II superconductors with strong line disorder directed {\it perpendicularly} to an applied field, the continuous vortex-glass transition is depressed to the low $T$ limit in the limit of weak {\it point} disorder. An anomalous resistive broadening in twin-free YBCO with columnar defects in a field parallel to the layers is discussed based on this theoretical finding. Other phenomena which, we argue, arise indirectly from this mechanism in type II superconductors including correlated defects are also discussed.

Vortex-glass transition and vortex phase diagram in a thick amorphous Mg xB 1− x film

We present superconducting properties and vortex states in a thick amorphous Mg x B 1− x film with x=0.31. Measurements of dc and ac complex resistivities in the mixed state reveal the presence of the vortex-glass transition in three dimensions. Based on the data, we construct the vortex phase diagram in the field–temperature plane. We find that there is the relatively large vortex-liquid phase, which persists down to low temperatures.

Dynamics of the vortex glass in the Corbino disk geometry

Dynamics of vortex glass (VG) driven by the current is studied based on current–voltage ( I– V) characteristics for a thick amorphous Mo x Si 1 − x film with Corbino-disk (CD) and strip-like contact geometries. In the VG phase the anomaly in the I– V curves is visible at certain current for the CD geometry, which is interpreted in terms of the spatial development of plastic flow motion of driven VG. The anomaly becomes less remarkable at higher temperature ( T) and at fixed T it disappears in the high-field ( B) region just above the VG transition ( B g) and in the low- B region well below B g.

Observation of flux flow based on vortex-glass scaling analysis for single phase HgBa 2Ca 2Cu 3O 8+ δ superconductor

A single phase HgBa 2Ca 2Cu 3O 8+ δ superconductor, having a T c of 133 K, was successfully synthesized. Electrical resistivity and critical current density measurements were performed. With the experiments of flux motion, it became clear that there is actually a more subtle shape to the I– V curve, or the ρ– T curve: separate regions of flux creep and flux flow can be identified according to the two universal curves, indicating a vortex-glass transition. This paper reports the ρ– T curves collapse on to the positive curvature line, associating with flux flow. The phase diagram in H– T space for the vortex-lattice can also show a vortex-glass–liquid transition at temperature T g.

Critical currents at the bragg glass to vortex glass transition.

We present simulations of the transport properties of superconductors at the transition from the Bragg glass (BG) to the vortex glass (VG) phase. We study the frustrated anisotropic 3D XY model with point disorder, which has been shown to have a first-order transition as a function of the intensity of disorder. We add an external current to the model, and we obtain current-voltage curves as a function of disorder at a low temperature. We find that the in-plane critical current has a steep increase at the BG-VG transition, while the c-axis critical current has a discontinuous jump down, this later result in agreement with the first-order character of the transition.

Effect of Ca doping in YBCO superconducting thin films

We investigate the effect of partial substitution of Y by Ca in YBCO superconducting thin films. The films were grown on (1 0 0) SrTiO3 single crystal substrates by pulsed laser deposition (PLD). The Ca doped film were ablated from Y1−xCaxBa2Cu3O7−δ targets with x=0, 0.05, 0.07, and 0.10. The dc transport properties of the films in applied magnetic field are analyzed to study the role of Ca on the superconducting properties of YBCO films. The irreversibility line for the samples with x=0 and 5 at.% Ca was derived from the E–J curves using a scaling theory for the vortex-glass transition.

Quantum Resistive Behaviors in Vortex Liquid Regimes at Finite Temperatures

Motivated by a {\it mean field-like} resistive behavior in magnetic fields commonly seen in various superconducting (SC) cuprates and organics with strong fluctuation, {\it quantum} SC fluctuation effects on resistive behaviors are reexamined by putting emphasis on their roles in the so-called {\it thermal} vortex liquid regime. By incorporating the quantum fluctuation and a vortex pinning effect in the GL fluctuation theory, it is found that the resistivity curve shows not a fan-shaped broadening but a sharp drop at a 3d vortex-glass transition point far below an apparent upper critical field H_{c2}^*(T) as a result of a quantm fluctuation enhanced by an adequately small condensation energy or by a strong field. Fittings to data of cuprate and organic superconductors are performed by including effects of SC pseudogap region. It is argued on the cuprate materials that, irrespective of the presence of fluctuations of competing non-SC orders, the in-plane coherence length of hole-doped cuprates decreases on approaching the underdoped limit and that the condensation energy density to be measured from the heat capacity data is maximum near the optimal doping. The case of disordered quasi 2d s-wave films showing the field-tuned superconductor-insulator transition (FSIT) behavior is also studied for comparison, and an agreement with available data is found.

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.

Vortex glass transition in a frustrated 3D XY model with disorder.

The anisotropic frustrated three-dimensional (3D) XY model with disorder in the coupling constants is simulated as a model of a point disordered superconductor in an applied magnetic field. A finite size scaling analysis of the helicity modulus gives strong evidence for a finite temperature transition with isotropic scaling and the correlation length exponent nu=1.5+/-0.3, consistent with 3D gauge glass universality.