Vortex-glass phases in type-II superconductors

A review is given on the theory of vortex-glass phases in impure type-II superconductors in an external field. We begin with a brief discussion of the effects of thermal fluctuations on the spontaneously broken U(1) and translation symmetries, on the global phase diagram and on the critical behaviour. Introducing disorder we restrict ourselves to the experimentally most relevant case of weak uncorrelated randomness which is known to destroy the long-ranged translational order of the Abrikosov lattice in three dimensions. Elucidating possible residual glassy ordered phases, we distinguish betwee positional and phase-coherent vortex glasses. The discussion of elastic vortex glasses, in two and three dimensions occupy the main part of our review. In particular, in three dimensions there exists an elastic vortex-glass phase which still shows quasi-long-range translational order: the `Bragg glass'. It is shown that this phase is stable with respect to the formation of dislocations for intermediate fields. Preliminary results suggest that the Bragg-glass phase may not show phase-coherent vortex-glass order. The latter is expected to occur in systems with weak disorder only in higher dimensions. We further demonstrate that the linear resistivity vanishes in the vortex-glass phase. The vortex-glass transition is studied in detail for a superconducting film in a parallel field. Finally, we review some recent developments concerning driven vortex-line lattices moving in a random environment.Comment: 133 pages Latex with figures. accepted for publication in Adv. Phy

Driven Dynamics of Periodic Elastic Media in Disorder

We analyze the large-scale dynamics of vortex lattices and charge density waves driven in a disordered potential. Using a perturbative coarse-graining procedure we present an explicit derivation of non-equilibrium terms in the renormalized equation of motion, in particular Kardar-Parisi-Zhang non-linearities and dynamic strain terms. We demonstrate the absence of glassy features like diverging linear friction coefficients and transverse critical currents in the drifting state. We discuss the structure of the dynamical phase diagram containing different elastic phases very small and very large drive and plastic phases at intermediate velocity.Comment: 21 pages Latex with 4 figure

Pinning Induced Fluctuations on Driven Vortices

We use a simple model to study the long time fluctuations induced by random pinning on the motion of driven non--interacting vortices. We find that vortex motion seen from the co--moving frame is diffusive and anisotropic, with velocity dependent diffusion constants. Longitudinal and transverse diffusion constants cross at a characteristic velocity where diffusion is isotropic. The diffusion front is elongated in the direction of the drive at low velocities and elongated in the transverse direction at large velocities. We find that the mobility in the driven direction is always larger than the transverse mobility, and becomes isotropic only in the large velocity limit.Comment: 4 pages, 3 figs, Vortex IV Proceedings, Sep. 3-9, 2005, Crete, Greec

Correlations in noisy Landau-Zener transitions

We analyze the influence of classical Gaussian noise on Landau-Zener transitions during a two-level crossing in a time-dependent regular external field. Transition probabilities and coherence factors become random due to the noise. We calculate their two-time correlation functions, which describe the response of this two-level system to a weak external pulse signal. The spectrum and intensity of the magnetic response are derived. Although fluctuations are of the same order of magnitude as averages, the results is obtained in an analytic form.Comment: 12 pages LaTex with 6 EPS figure

Elastic theory of quantum Hall smectics: effects of disorder

We study the effect of disorder on quantum Hall smectics within the framework of an elastic theory. Based on a renormalization group calculation, we derive detailed results for the degrees of translational and orientational order of the stripe pattern at zero temperature and carefully map out the disorder and length-scale regimes in which the system effectively exhibits smectic, nematic, or isotropic behavior. We show that disorder always leads to a finite density of free dislocations and estimate the scale on which they begin to appear.Comment: 4 pages latex with 1 EPS figur

Frustrated Heisenberg antiferromagnets: fluctuation induced first order vs deconfined quantum criticality

Recently it was argued that quantum phase transitions can be radically different from classical phase transitions with as a highlight the 'deconfined critical points' exhibiting fractionalization of quantum numbers due to Berry phase effects. Such transitions are supposed to occur in frustrated ('$J_1$-$J_2$') quantum magnets. We have developed a novel renormalization approach for such systems which is fully respecting the underlying lattice structure. According to our findings, another profound phenomenon is around the corner: a fluctuation induced (order-out-of-disorder) first order transition. This has to occur for large spin and we conjecture that it is responsible for the weakly first order behavior recently observed in numerical simulations for frustrated $S=1/2$ systems.Comment: 7 pages, 3 Figures, submitted to EP