Vortices freeze like window glass: the vortex molasses scenario

Vortex Glass-Vortex Liquid Transition in BaFe2(As1-xPx)2 and CaKFe4As4 Superconductors from Multi-Harmonic AC Magnetic Susceptibility Studies

For practical applications of superconductors, understanding the vortex matter and dynamics is of paramount importance. An important issue in this context is the transition of the vortex glass, which is a true superconducting phase, into a vortex liquid phase having a linear dissipation. By using multi-harmonic susceptibility studies, we have investigated the vortex glass-vortex liquid phase transitions in CaKFe4As4 and BaFe2(As0.68P0.32)2 single crystals. The principle of our method relates the on-set of the third-harmonic susceptibility response with the appearance of a vortex-glass phase in which the dissipation is non-linear. Similar to the high-critical temperature cuprate superconductors, we have shown that even in these iron-based superconductors with significant lower critical temperatures, such phase transition can be treated as a melting in the sense of Lindemann's approach, considering an anisotropic Ginzburg-Landau model. The experimental data are consistent with a temperature-dependent London penetration depth given by a 3D XY fluctuations model. The fitting parameters allowed us to extrapolate the vortex melting lines down to the temperature of liquid hydrogen, and such extrapolation showed that CaKFe4As4 is a very promising superconducting material for high field applications in liquid hydrogen, with a melting field at 20 K of the order of 100 T.

Dynamics of nanoscale polarization fluctuations in a uniaxial relaxor

We have studied neutron diffuse scattering in a Sr(0.61)Ba(0.39)Nb(2)O(6) single crystal by neutron backscattering at sub-μeV energy resolution. We can identify two response components with transverse polarization: an elastic (resolution limited) central peak, which monotonically increases with decreasing temperature, and a quasielastic central peak, having a maximum intensity around the ferroelectric phase transition close to 350 K. In contrast to previous neutron experiments on this and other relaxor materials, we were able to observe a temperature dependence of the characteristic frequency of these fluctuations, obeying the same Vogel-Fulcher law as the dynamic part of the dielectric permittivity of this material. In this way our findings provide a first direct link between the Vogel-Fulcher-type frequency dependence of dielectric permittivity and dynamic nanoscale lattice modulations with a transverse correlation length of about 5-10 unit cells.

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.

Equilibrium first-order melting and second-order glass transitions of the vortex matter in Bi2Sr2CaCu2O8

The thermodynamic phase diagram of Bi2Sr2CaCu2O8 was mapped by measuring local equilibrium magnetization M(H,T) in the presence of vortex shaking. Two equally sharp first-order magnetization steps are revealed in a single temperature sweep, manifesting a liquid-solid-liquid sequence. In addition, a second-order glass transition line is revealed by a sharp break in the equilibrium M(T) slope. The first- and second-order lines intersect at intermediate temperatures, suggesting the existence of four phases: Bragg glass and vortex crystal at low fields, glass and liquid at higher fields.

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.

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.

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.

Theory of the vortex matter transformations in high-Tc superconductor YBCO

Flux line lattice in type II superconductors undergoes a transition into a "disordered" phase such as vortex liquid or vortex glass, due to thermal fluctuations and random quenched disorder. We quantitatively describe the competition between the thermal fluctuations and the disorder using the Ginzburg-Landau approach. The following T-H phase diagram of YBCO emerges. There are just two distinct thermodynamical phases, the homogeneous and the crystalline one, separated by a single first order transition line. The line, however, makes a wiggle near the experimentally claimed critical point at 12 T. The "critical point" is reinterpreted as a (noncritical) Kauzmann point in which the latent heat vanishes and the line is parallel to the T axis. The magnetization, the entropy, and the specific heat discontinuities at melting compare well with experiments.

Intrinsic behavior of flux lines in pure niobium near the upper critical field

We report small-angle neutron-scattering (SANS) measurements of flux line properties near H(c2) in an ultrapure sample of niobium with weak pinning of flux in the bulk. These confirm in detail the Abrikosov picture of the flux line lattice to within 20 mK of the upper critical field line. However, it has recently been claimed [X. S. Ling et al., Phys. Rev. Lett. 86, 712 (2001)], on the basis of SANS observations of a disordering of flux lines in niobium, that the flux lattice melts at temperatures clearly separated from the upper critical field line. This discrepancy may possibly arise from differences in sample purity and pinning.

Vortex glass transition in a random pinning model

We study the vortex glass transition in disordered high temperature superconductors using Monte Carlo simulations. We use a random pinning model with strong point-correlated quenched disorder, a net applied magnetic field, long-range vortex interactions, and periodic boundary conditions. From a finite size scaling study of the helicity modulus, the rms current, and the resistivity, we obtain critical exponents at the phase transition. The new exponents differ substantially from those of the gauge glass model, but are close to those of the pure three-dimensional XY model.

Disorder driven melting of the vortex line lattice

The 3D XY model with random in-plane couplings is simulated to model the phase diagram of a disordered type II superconductor as a function of temperature T and randomness strength p for fixed applied magnetic field. As p increases to a critical p(c), the first order vortex lattice melting line turns parallel to the T axis, continuing down to low temperatures, rather than ending at a critical point. Above p(c) preliminary results suggest the absence of a phase coherent vortex glass.

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.

'Inverse' melting of a vortex lattice

Inverse melting is the process in which a crystal reversibly transforms into a liquid or amorphous phase when its temperature is decreased. Such a process is considered to be very rare, and the search for it is often hampered by the formation of non-equilibrium states or intermediate phases. Here we report the discovery of first-order inverse melting of the lattice formed by magnetic flux lines in a high-temperature superconductor. At low temperatures, disorder in the material pins the vortices, preventing the observation of their equilibrium properties and therefore the determination of whether a phase transition occurs. But by using a technique to 'dither' the vortices, we were able to equilibrate the lattice, which enabled us to obtain direct thermodynamic evidence of inverse melting of the ordered lattice into a disordered vortex phase as the temperature is decreased. The ordered lattice has larger entropy than the low-temperature disordered phase. The mechanism of the first-order phase transition changes gradually from thermally induced melting at high temperatures to a disorder-induced transition at low temperatures.

Effects of point defects on the phase diagram of vortex states in high- T(c) superconductors in the B parallel to c axis

The phase diagram for the vortex states of high- T(c) superconductors with point defects in the B--> parallel to c axis is drawn by large-scale Monte Carlo simulations. The vortex slush (VS) phase is found between the vortex glass (VG) and vortex liquid (VL) phases. The first-order transition between this novel normal phase and the VL phase is characterized by a sharp jump of the density of dislocations. The first-order transition between the Bragg glass (BG) and VG or VS phases is also clarified. These two transitions are compared with the melting transition between the BG and VL phases.

An unusual phase transition to a second liquid vortex phase in the superconductor YBa2Cu3O7

A magnetic field penetrates a superconductor through an array of 'vortices', each of which carries one quantum of flux that is surrounded by a circulating supercurrent. In this vortex state, the resistivity is determined by the dynamical properties of the vortex 'matter'. For the high-temperature copper oxide superconductors (see ref.1 for a theoretical review), the vortex phase can be a 'solid', in which the vortices are pinned, but the solid can 'melt' into a 'liquid' phase, in which their mobility gives rise to a finite resistance. (This melting phenomenon is also believed to occur in conventional superconductors, but in an experimentally inaccessible part of the phase diagram.) For the case of YBa2Cu3O7, there are indications of the existence of a critical point, at which the character of the melting changes. But neither the thermodynamic nature of the melting, nor the phase diagram in the vicinity of the critical point, has been well established. Here we report measurements of specific heat and magnetization that determine the phase diagram in this material to 26 T, well above the critical point. Our results reveal the presence of a reversible second-order transition above the critical point. An unusual feature of this transition-namely, that the high-temperature phase is the less symmetric in the sense of the Landau theory-is in accord with theoretical predictions of a transition to a second vortex-liquid phase.

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.

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.