P. Le Doussal

PHASE DIAGRAMS OF FLUX LATTICES WITH DISORDER

We review the prediction, made in a previous work [Phys. Rev. B 52 (1995)], that the phase diagram of type II superconductors consists of a topologically ordered Bragg glass phase at low fields undergoing a transition at higher fields into a vortex glass or a liquid. We estimate the position of the phase boundary using a Lindemann criterion. We find that the proposed phenomenology is compatible with recent experiments on superconductors.

Classical diffusion of a particle in a one-dimensional random force field

Abstract We present a comprehensive study of the motion of a damped Brownian particle evolving in a static, one dimensional gaussian random force field. We provide both a clear physical picture of the process and a variety of analytical techniques. As the average bias μ is increased, a succession of different “diffusion laws” is observed: Sinais diffusion ( μ = 0, x 2 ⋍ ln 4 t ), anomalous drift ( x ⋍ t μ , μ ), anomalous dispersion ( x − Vt ⋍ ±t 1 μ , 1 ), and finally normal diffusion (μ > 2), apart from algebraic tails outside the scaling region. We show that all those results can be understood in simple terms through a large scale description of the problem as a directed walk among traps characterized by a broad distribution of release time. From this analysis, the full asymptotic probability distributions (averaged over disorder) are precisely determined, in terms of Levy stable laws. Sample to sample fluctuations are discussed. The probability of presence at the initial point is more specifically adressed. It amounts to computing the density of states of a Schrodinger equation with a special type of random potential. We obtain exactly the average over disorder of this quantity, using the following two different approaches: the “Dyson-Schmidt” technique, and the replica method. Both reveal interesting technical features, and the latter can be used to obtain information on the full probability distribution (and Green function). Some physical applications of this model are discussed.

Gauge field induced by ripples in graphene

We study the effects of quenched height fluctuations (ripples) in graphene on the density of states (DOS). We show that at strong ripple disorder, a divergence in the DOS can lead to an ordered ground state. We also discuss the formation of dislocations in corrugated systems, buckling effects in suspended samples, and the changes in the Landau levels due to the interplay between a real magnetic field and the gauge potential induced by ripples.

Moving glass phase of driven lattices.

We study periodic lattices, such as vortex lattices, driven by an external force in a random pinning potential. We show that effects of static disorder persist even at large velocity. It results in a novel moving glass state which has analogies with the static Bragg glass. The lattice flows through well-defined, elastically coupled, {ital static} channels. We predict barriers to transverse motion resulting in finite transverse critical current. Experimental tests of the theory are proposed. {copyright} {ital 1996 The American Physical Society.}

A Bragg glass phase in the vortex lattice of a type II superconductor.

Although crystals are usually quite stable, they are sensitive to a disordered environment: even an infinitesimal amount of impurities can lead to the destruction of crystalline order. The resulting state of matter has been a long-standing puzzle. Until recently it was believed to be an amorphous state in which the crystal would break into ‘crystallites’. But a different theory predicts the existence of a novel phase of matter: the so-called Bragg glass, which is a glass and yet nearly as ordered as a perfect crystal. The ‘lattice’ of vortices that contain magnetic flux in type II superconductors provide a good system to investigate these ideas. Here we show that neutron-diffraction data of the vortex lattice provides unambiguous evidence for a weak, power-law decay of the crystalline order characteristic of a Bragg glass. The theory also predicts accurately the electrical transport properties of superconductors; it naturally explains the observed phase transitions and the dramatic jumps in the critical current associated with the melting of the Bragg glass. Moreover, the model explains experiments as diverse as X-ray scattering in disordered liquid crystals and the conductivity of electronic crystals.

Creep via dynamical functional renormalization group

We study a D-dimensional interface driven in a disordered medium. We derive finite-temperature and velocity functional renormalization group (FRG) equations, valid in a = 4 − D expansion. These equations allow in principle for a complete study of the velocity v vs. applied force density f characteristics. We focus here on the creep regime at finite temperature and small velocity. We show how the FRG approach gives the form of the v-f characteristics in this regime, and in particular the creep exponent, obtained previously only through phenomenological scaling arguments.

Height fluctuations of a contact line: A direct measurement of the renormalized disorder correlator

We measure the center-of-mass fluctuations of the height of a contact line at depinning for two different systems: liquid hydrogen on a rough cesium substrate and isopropanol on a silicon wafer grafted with silanized patches. The contact line is subject to a confining quadratic well, provided by gravity. From the second cumulant of the height fluctuations, we measure the renormalized disorder correlator Δ(u), predicted by Functional RG to attain a fixed point, as soon as the capillary length is large compared to the Larkin length set by the microscopic disorder. The experiments are consistent with the asymptotic form for Δ(u) predicted by Functional RG, including a linear cusp at u=0. The observed small deviations could be used as a probe of the underlying physical processes. The third moment, as well as avalanche-size distributions are measured and compared to predictions from Functional RG.

Self-Avoiding Walks in Quenched Random Environments

The self-avoiding walk in a quenched random environment is studied using real-space and field-theoretic renormalization and “Flory” arguments. These methods indicate that the system is described, forddc, by a strong disorder fixed point corresponding to a “glass” state in which the polymer is confined to the lowest energy path. This fixed point is characterized by scaling laws for the size of the walk,L∼Npζ withN the number of steps, and the fluctuations in the free energy,Αf∼Lpζ. The bound 1/ζ-ω⩽d/2 is obtained. Exact results on hierarchical lattices yieldζ>ζpure and suggests that this inequality holds ford=2 and 3, althoughζ=ζpure cannot be excluded, particularly ford=2. Ford>dc there is a transition between strong and weak disorder phases at whichζ=ζpure. The strong-disorder fixed point for SAWs on percolation clusters is discussed. The analogy with directed walks is emphasized.

Stability of the Bragg glass phase in a layered geometry

We study the stability of the dislocation-free Bragg glass phase in a layered geometry consisting of coupled parallel planes of d = 1 + 1 vortex lines lying within each plane, in the presence of impurity disorder. Using renormalization group, replica variational calculations and physical arguments, we find that at temperatures T < TG the 3D Bragg glass phase is always stable for weak disorder. It undergoes a weakly first-order transition into a decoupled 2D vortex glass upon increase of disorder.

DYNAMICAL PROPERTIES OF THE PINNED WIGNER CRYSTAL

We study various dynamical properties of the weakly pinned Wigner crystal in a high magnetic field. Using a Gaussian variational method we can compute the full frequency and field dependence of the real and imaginary parts of the diagonal and Hall conductivities. The zero temperature Hall resistivity is independent of frequency and remains unaffected by disorder at its classical value. We show that, depending on the inherent length scales of the system, the pinning peak and the threshold electric field exhibit strikingly different magnetic field dependences.