V-I characteristics in the vicinity of order-disorder transition in vortex matter

The shape of the V-I characteristics leading to a peak in the differential resistance r_d=dV/dI in the vicinity of the order-disorder transition in NbSe2 is investigated. r_d is large when measured by dc current. However, for a small Iac on a dc bias r_d decreases rapidly with frequency, even at a few Hz, and displays a large out-of-phase signal. In contrast, the ac response increases with frequency in the absence of dc bias. These surprisingly opposite phenomena and the peak in r_d are shown to result from a dynamic coexistence of two vortex matter phases rather than from the commonly assumed plastic depinning.Comment: 12 pages 4 figures. Accepted for publication in PRB rapi

Square Patterns and Quasi-patterns in Weakly Damped Faraday Waves

Pattern formation in parametric surface waves is studied in the limit of weak viscous dissipation. A set of quasi-potential equations (QPEs) is introduced that admits a closed representation in terms of surface variables alone. A multiscale expansion of the QPEs reveals the importance of triad resonant interactions, and the saturating effect of the driving force leading to a gradient amplitude equation. Minimization of the associated Lyapunov function yields standing wave patterns of square symmetry for capillary waves, and hexagonal patterns and a sequence of quasi-patterns for mixed capillary-gravity waves. Numerical integration of the QPEs reveals a quasi-pattern of eight-fold symmetry in the range of parameters predicted by the multiscale expansion.Comment: RevTeX, 11 pages, 8 figure

Critical depinning force and vortex lattice order in disordered superconductors

We simulate the ordering of vortices and its effects on the critical current in superconductors with varied vortex-vortex interaction strength and varied pinning strengths for a two-dimensional system. For strong pinning the vortex lattice is always disordered and the critical depinning force only weakly increases with decreasing vortex-vortex interactions. For weak pinning the vortex lattice is defect free until the vortex-vortex interactions have been reduced to a low value, when defects begin to appear with a simultaneous rapid increase in the critical depinning force. In each case the depinning force shows a maximum for non-interacting vortices. The relative height of the peak increases and the peak width decreases for decreasing pinning strength in excellent agreement with experimental trends associated with the peak effect. We show that scaling relations exist between the distance between defects in the vortex lattice and the critical depinning force.Comment: 5 pages, 6 figure

Transverse depinning in strongly driven vortex lattices with disorder

Using numerical simulations we investigate the transverse depinning of moving vortex lattices interacting with random disorder. We observe a finite transverse depinning barrier for vortex lattices that are driven with high longitudinal drives, when the vortex lattice is defect free and moving in correlated 1D channels. The transverse barrier is reduced as the longitudinal drive is decreased and defects appear in the vortex lattice, and the barrier disappears in the plastic flow regime. At the transverse depinning transition, the vortex lattice moves in a staircase pattern with a clear transverse narrow-band voltage noise signature.Comment: 4 pages, 4 figure

Berry Curvature in Graphene: A New Approach

In the present paper we have directly computed the Berry curvature terms relevant for Graphene in the presence of an \textit{inhomogeneous} lattice distortion. We have employed the generalized Foldy Wouthuysen framework, developed by some of us \cite{ber0,ber1,ber2}. We show that a non-constant lattice distortion leads to a valley-orbit coupling which is responsible to a valley-Hall effect. This is similar to the valley-Hall effect induced by an electric field proposed in \cite{niu2} and is the analogue of the spin-Hall effect in semiconductors \cite{MURAKAMI, SINOVA}. Our general expressions for Berry curvature, for the special case of homogeneous distortion, reduce to the previously obtained results \cite{niu2}. We also discuss the Berry phase in the quantization of cyclotron motion.Comment: Slightly modified version, to appear in EPJ

Critical Currents and Vortex States at Fractional Matching Fields in Superconductors with Periodic Pinning

We study vortex states and dynamics in 2D superconductors with periodic pinning at fractional sub-matching fields using numerical simulations. For square pinning arrays we show that ordered states form at 1/1, 1/2, and 1/4 filling fractions while only partially ordered states form at other filling fractions, such as 1/3 and 1/5, in agreement with recent imaging experiments. For triangular pinning arrays we observe matching effects at filling fractions of 1/1, 6/7, 2/3, 1/3, 1/4, 1/6, and 1/7. For both square and triangular pinning arrays we also find that, for certian sub-matching fillings, vortex configurations depend on pinning strength. For weak pinning, ordering in which a portion of the vortices are positioned between pinning sites can occur. Depinning of the vortices at the matching fields, where the vortices are ordered, is elastic while at the incommensurate fields the motion is plastic. At the incommensurate fields, as the applied driving force is increased, there can be a transition to elastic flow where the vortices move along the pinning sites in 1D channels and a reordering transition to a triangular or distorted triangular lattice. We also discuss the current-voltage curves and how they relate to the vortex ordering at commensurate and incommensurate fields.Comment: 14 figure

Interaction of Nearly-Inviscid, Multi-mode Faraday Waves and Mean Flows

Faraday waves [1] are gravity-capillary waves that are excited on the surface of a fluid when its container is vibrated vertically and the vertical acceleration exceeds a threshold value. These waves have received much attention in the literature both as a basic fluid dynamical problem and as a paradigm of a pattern-forming system [2-4]. Unfortunately, in the low viscosity limit, there are several basic issues that remain unresolved, particularly in connection with the generation of mean flows in the bulk. The viscous part of these flows (also called streaming flow or acoustic streaming) is driven by the oscillatory boundary layers attached to the solid walls and the free surface by well-known mechanisms first uncovered by Schlichting [5] and Longuet-Higgins [6]. This mean flow has been shown recently to affect the dynamics of the primary waves at leading order in a related, laterally vibrated system [7]. This is somewhat similar to the effect of an internal circulation on surface wave dynamics in drops [8]

Metastability and Transient Effects in Vortex Matter Near a Decoupling Transition

We examine metastable and transient effects both above and below the first-order decoupling line in a 3D simulation of magnetically interacting pancake vortices. We observe pronounced transient and history effects as well as supercooling and superheating between the 3D coupled, ordered and 2D decoupled, disordered phases. In the disordered supercooled state as a function of DC driving, reordering occurs through the formation of growing moving channels of the ordered phase. No channels form in the superheated region; instead the ordered state is homogeneously destroyed. When a sequence of current pulses is applied we observe memory effects. We find a ramp rate dependence of the V(I) curves on both sides of the decoupling transition. The critical current that we obtain depends on how the system is prepared.Comment: 10 pages, 15 postscript figures, version to appear in PR

Velocity-force characteristics of an interface driven through a periodic potential

We study the creep dynamics of a two-dimensional interface driven through a periodic potential using dynamical renormalization group methods. We find that the nature of weak-drive transport depends qualitatively on whether the temperature $T$ is above or below the equilibrium roughening transition temperature $T_c$. Above $T_c$, the velocity-force characteristics is Ohmic, with linear mobility exhibiting a jump discontinuity across the transition. For $T \le T_c$, the transport is highly nonlinear, exhibiting an interesting crossover in temperature and weak external force $F$. For intermediate drive, $F>F_*$, we find near $T_c^{-}$ a power-law velocity-force characteristics $v(F)\sim F^\sigma$, with $\sigma-1\propto \tilde{t}$, and well-below $T_c$, $v(F)\sim e^{-(F_*/F)^{2\tilde{t}}}$, with $\tilde{t}=(1-T/T_c)$. In the limit of vanishing drive ($F\ll F_*$) the velocity-force characteristics crosses over to $v(F)\sim e^{-(F_0/F)}$, and is controlled by soliton nucleation.Comment: 18 pages, submitted to Phys. Rev.