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In a recent letter Klein et al. [Nature 413, 404 (2001); cond-mat/0110018] provide experimental evidence for the existence of the Bragg glass phase in impure type II superconductors. Here we show that a more complete consideration of recent theoretical findings allows an even better interpretation of the experimental data.
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The order of the vortex state in La_{1.9} Sr_{0.1} CuO_{4} is probed using muon spin rotation and small-angle neutron scattering. A transition from a Bragg glass to a vortex glass is observed, where the latter is composed of disordered vortex lines. In the vicinity of the transition the microscopic behavior reflects a delicate interplay of thermally-induced and pinning-induced disorder.
Order-disorder transitions between glassy phases are quite common in nature and yet a comprehensive survey of the microscopic structural changes remains elusive since the scale of the constituents is tiny and in most cases few of them take part in the transformation. Vortex matter in type-II superconductors is a model system where some of the experimental challenges inherent to this general question can be tackled by adequately choosing the host superconducting sample. For instance, Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8 + delta}$ is a type-II superconductor with weak point disorder that presents a transition between two glassy phases on increasing the constituents (vortices) density. At low vortex densities, the impact of disorder produces the nucleation of a glassy yet quasi-crystalline phase, the Bragg glass. For high vortex densities the stable phase, coined as $textit{vortex glass}$, was proposed to be disordered, but its structural properties have remained elusive up to now. Here we answer this question by combining surface and bulk vortex imaging techniques, and show that the vortex glass is neither a messy nor a hexatic phase: in the plane of vortices it presents large crystallites with positional correlations growing algebraically and short-ranged orientational order. However, no dramatic change in the correlation length along the direction of vortices is observed on traversing the order-disorder transformation.
We have used small-angle-neutron-scattering (SANS) and ac magnetic susceptibility to investigate the global magnetic field H vs temperature T phase diagram of a single crystal Nb in which a first-order transition of Bragg-glass melting (disordering), a peak effect, and surface superconductivity are all observable. It was found that the disappearance of the peak effect is directly related to a multicritical behavior in the Bragg-glass transition. Four characteristic phase boundary lines have been identified on the H-T plane: a first-order line at high fields, a mean-field-like continuous transition line at low fields, and two continuous transition line associated with the onset of surface and bulk superconductivity. All four lines are found to meet at a multicritical point.
The breakdown of crystalline order in a disordered background connects to some of the most challenging problems in condensed matter physics. For a superconducting vortex lattice, the equilibrium state in the presence of impurities is predicted to be a Bragg glass (BG), where the local crystalline order is maintained everywhere and yet the global positional order decays algebraically. Here, using scanning tunnelling spectroscopy (STS) we image the vortex lattice in a weakly pinned NbSe2 single crystal. We present direct evidence that the ordered state of the VL is a BG, consisting of a large number of degenerate metastable states, which is a hallmark of a glassy state. These results are a significant step towards understanding the disordering of a lattice under the influence of quenched random disorder with a direct impact on various fields, including charge density waves, colloidal crystals and self-organised periodic structures on a substrate.
Dynamics of vortices in strongly type-II superconductors with strong disorder is investigated within the frustrated three-dimensional XY model. For two typical models in [Phys. Rev. Lett. {bf 91}, 077002 (2003)] and [Phys. Rev. B {bf 68}, 220502(R) (2003)], a strong evidence for the finite temperature vortex glass transition in the unscreened limit is provided by performing large-scale dynamical simulations. The obtained correlation length exponents and the dynamic exponents in both models are different from each other and from those in the three-dimensional gauge glass model. In addition, a genuine continuous depinning transition is observed at zero temperature for both models. A scaling analysis for the thermal rounding of the depinning transition shows a non-Arrhenius type creep motion in the vortex glass phase, contrarily to the recent studies..
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