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

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

Rectification in Luttinger liquids

We investigate the rectification of an ac bias in Luttinger liquids in the presence of an asymmetric potential (the ratchet effect). We show that strong repulsive electron interaction enhances the ratchet current in comparison with Fermi liquid systems, and the I-V curve is strongly asymmetric in the low-voltage regime even for a weak asymmetric potential. At higher voltages the ratchet current exhibits an oscillatory voltage dependence.Comment: 5 pages, Revte

Nonequilibrium dislocation dynamics and instability of driven vortex lattices in two dimensions

We consider dislocations in a vortex lattice that is driven in a two-dimensional superconductor with random impurities. The structure and dynamics of dislocations is studied in this genuine nonequilibrium situation on the basis of a coarse-grained equation of motion for the displacement field. The presence of dislocations leads to a characteristic anisotropic distortion of the vortex density that is controlled by a Kardar-Parisi-Zhang nonlinearity in the coarse-grained equation of motion. This nonlinearity also implies a screening of the interaction between dislocations and thereby an instability of the vortex lattice to the proliferation of free dislocations.Comment: published version with minor correction

Hall noise and transverse freezing in driven vortex lattices

We study driven vortices lattices in superconducting thin films. Above the critical force $F_c$ we find two dynamical phase transitions at $F_p$ and $F_t$, which could be observed in simultaneous noise measurements of the longitudinal and the Hall voltage. At $F_p$ there is a transition from plastic flow to smectic flow where the voltage noise is isotropic (Hall noise = longitudinal noise) and there is a peak in the differential resistance. At $F_t$ there is a sharp transition to a frozen transverse solid where the Hall noise falls down abruptly and vortex motion is localized in the transverse direction.Comment: 4 pages, 3 figure