Current-induced anisotropy and reordering of the electron liquid-crystal phases in a two-dimensional electron system

Peak effect and dynamics of stripe- and pattern-forming systems on a periodic one-dimensional substrate

We examine the ordering, pinning, and dynamics of two-dimensional pattern-forming systems interacting with a periodic one-dimensional substrate. In the absence of the substrate, particles with competing long-range repulsion and short-range attraction form anisotropic crystal, stripe, and bubble states. When the system is tuned across the stripe transition in the presence of a substrate, we find that there is a peak effect in the critical depinning force when the stripes align and become commensurate with the substrate. Under an applied drive, the anisotropic crystal and stripe states can exhibit soliton depinning and plastic flow. When the stripes depin plastically, they dynamically reorder into a moving stripe state that is perpendicular to the substrate trough direction. We also find that when the substrate spacing is smaller than the widths of the bubbles or stripes, the system forms pinned stripe states that are perpendicular to the substrate trough direction. The system exhibits multiple reentrant pinning effects as a function of increasing attraction, with the anisotropic crystal and large bubble states experiencing weak pinning but the stripe and smaller bubble states showing stronger pinning. We map out the different dynamic phases as a function of filling, the strength of the attractive interaction term, the substrate strength, and the drive, and demonstrate that the different phases produce identifiable features in the transport curves and particle orderings.

Straight motion of half-integer topological defects in thin Fe-N magnetic films with stripe domains

In thin magnetic films with perpendicular magnetic anisotropy, a periodic “up-down” stripe-domain structure can be originated at remanence, on a mesoscopic scale (~100 nm) comparable with film thickness, by the competition between short-range exchange coupling and long-range dipolar interaction. However, translational order is perturbed because magnetic edge dislocations are spontaneously nucleated. Such topological defects play an important role in magnetic films since they promote the in-plane magnetization reversal of stripes and, in superconductor/ferromagnet hybrids, the creation of superconducting vortex clusters. Combining magnetic force microscopy experiments and micromagnetic simulations, we investigated the motion of two classes of magnetic edge dislocations, randomly distributed in an \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm{N}}}_{2}^{+}$$\end{document}N2+-implanted Fe film. They were found to move in opposite directions along straight trajectories parallel to the stripes axis, when driven by a moderate dc magnetic field. Using the approximate Thiele equation, analytical expressions for the forces acting on such magnetic defects and a microscopic explanation for the direction of their motion could be obtained. Straight trajectories are related to the presence of a periodic stripe domain pattern, which imposes the gyrotropic force to vanish even if a nonzero, half-integer topological charge is carried by the defects in some layers across the film thickness.

Competing Charge Density Waves Probed by Nonlinear Transport and Noise in the Second and Third Landau Levels

Charge density waves (CDWs) in the second and third Landau levels (LLs) are investigated by both nonlinear electronic transport and noise. The use of a Corbino geometry ensures that only bulk properties are probed, with no contribution from edge states. Sliding transport of CDWs is revealed by narrow band noise in reentrant quantum Hall states R2a and R2c of the second LL, as well as in pinned CDWs of the third LL. Competition between various phases-stripe, pinned CDW, or fractional quantum Hall liquid-in both LLs are clearly revealed by combining noise data with maps of conductivity versus magnetic field and bias voltage.

Current Flow in the Bubble and Stripe Phases

The spontaneous ordering of spins and charges in geometric patterns is currently under scrutiny in a number of different material systems. A topic of particular interest is the interaction of such ordered phases with itinerant electrons driven by an externally imposed current. It not only provides important information on the charge ordering itself but potentially also allows manipulating the shape and symmetry of the underlying pattern if current flow is strong enough. Unfortunately, conventional transport methods probing the macroscopic resistance suffer from the fact that the voltage drop along the sample edges provides only indirect information on the bulk properties because a complex current distribution is elicited by the inhomogeneous ground state. Here, we promote the use of surface acoustic waves to study these broken-symmetry phases and specifically address the bubble and stripe phases emerging in high-quality two-dimensional electron systems in GaAs/AlGaAs heterostructures as prototypical examples. When driving a unidirectional current, we find a surprising discrepancy between the sound propagation probing the bulk of the sample and the voltage drop along the sample edges. Our results prove that the current-induced modifications observed in resistive transport measurements are in fact a local phenomenon only, leaving the majority of the sample unaltered. More generally, our findings shed new light on the extent to which these ordered electron phases are impacted by an external current and underline the intrinsic advantages of acoustic measurements for the study of such inhomogeneous phases.

Possible nematic to smectic phase transition in a two-dimensional electron gas at half-filling

Liquid crystalline phases of matter permeate nature and technology, with examples ranging from cell membranes to liquid-crystal displays. Remarkably, electronic liquid-crystal phases can exist in two-dimensional electron systems (2DES) at half Landau-level filling in the quantum Hall regime. Theory has predicted the existence of a liquid-crystal smectic phase that breaks both rotational and translational symmetries. However, previous experiments in 2DES are most consistent with an anisotropic nematic phase breaking only rotational symmetry. Here we report three transport phenomena at half-filling in ultra-low disorder 2DES: a non-monotonic temperature dependence of the sample resistance, dramatic onset of large time-dependent resistance fluctuations, and a sharp feature in the differential resistance suggestive of depinning. These data suggest that a sequence of symmetry-breaking phase transitions occurs as temperature is lowered: first a transition from an isotropic liquid to a nematic phase and finally to a liquid-crystal smectic phase.

In the quantum Hall regime, strong interactions lead to the formation of unconventional spatially ordered electronic states. Qian et al. present evidence for a progressive sequence of transitions from isotropic through nematic to smectic phases in half-filled quantum Hall states.

Depinning and nonequilibrium dynamic phases of particle assemblies driven over random and ordered substrates: a review

We review the depinning and nonequilibrium phases of collectively interacting particle systems driven over random or periodic substrates. This type of system is relevant to vortices in type-II superconductors, sliding charge density waves, electron crystals, colloids, stripe and pattern forming systems, and skyrmions, and could also have connections to jamming, glassy behaviors, and active matter. These systems are also ideal for exploring the broader issues of characterizing transient and steady state nonequilibrium flow phases as well as nonequilibrium phase transitions between distinct dynamical phases, analogous to phase transitions between different equilibrium states. We discuss the differences between elastic and plastic depinning on random substrates and the different types of nonequilibrium phases which are associated with specific features in the velocity-force curves, fluctuation spectra, scaling relations, and local or global particle ordering. We describe how these quantities can change depending on the dimension, anisotropy, disorder strength, and the presence of hysteresis. Within the moving phase we discuss how there can be a transition from a liquid-like state to dynamically ordered moving crystal, smectic, or nematic states. Systems with periodic or quasiperiodic substrates can have multiple nonequilibrium second or first order transitions in the moving state between chaotic and coherent phases, and can exhibit hysteresis. We also discuss systems with competing repulsive and attractive interactions, which undergo dynamical transitions into stripes and other complex morphologies when driven over random substrates. Throughout this work we highlight open issues and future directions such as absorbing phase transitions, nonequilibrium work relations, inertia, the role of non-dissipative dynamics such as Magnus effects, and how these results could be extended to the broader issues of plasticity in crystals, amorphous solids, and jamming phenomena.

Electron-Hole Asymmetric Chiral Breakdown of Reentrant Quantum Hall States

Reentrant integer quantum Hall (RIQH) states are believed to be correlated electron solid phases, although their microscopic description remains unclear. As bias current increases, longitudinal and Hall resistivities measured for these states exhibit multiple sharp breakdown transitions, a signature unique to RIQH states. A comparison of RIQH breakdown characteristics at multiple voltage probes indicates that these signatures can be ascribed to a phase boundary between broken-down and unbroken regions, spreading chirally from source and drain contacts as a function of bias current and passing voltage probes one by one. The chiral sense of the spreading is not set by the chirality of the edge state itself, instead depending on electron- or holelike character of the RIQH state.

Stripe systems with competing interactions on quasi-one dimensional periodic substrates

We numerically examine the two-dimensional ordering of a stripe forming system of particles with competing long-range repulsion and short-range attraction in the presence of a quasi-one-dimensional corrugated substrate. As a function of increasing substrate strength or period we show that a remarkable variety of distinct orderings can be realized, including modulated stripes, prolate clump phases, two dimensional ordered kink structures, crystalline void phases, and smectic phases. Additionally in some cases the stripes align perpendicular to the substrate troughs. Our results suggest that a new route to self assembly for systems with competing interactions can be achieved through the addition of a simple periodic modulated substrate.

Anisotropic sliding dynamics, peak effect, and metastability in stripe systems

A variety of soft and hard condensed matter systems are known to form stripe patterns. Here we use numerical simulations to analyze how such stripe states depin and slide when interacting with a random substrate and with driving in different directions with respect to the orientation of the stripes. Depending on the strength and density of the substrate disorder, we find that there can be pronounced anisotropy in the transport produced by different dynamical flow phases. We also find a disorder-induced "peak effect" similar to that observed for superconducting vortex systems, which is marked by a transition from elastic depinning to a state where the stripe structure fragments or partially disorders at depinning. Under the sudden application of a driving force, we observe pronounced metastability effects similar to those found near the order-disorder transition associated with the peak effect regime for three-dimensional superconducting vortices. The characteristic transient time required for the system to reach a steady state diverges in the region where the flow changes from elastic to disordered. We also find that anisotropy of the flow persists in the presence of thermal disorder when thermally induced particle hopping along the stripes dominates. The thermal effects can wash out the effects of the quenched disorder, leading to a thermally induced stripe state. We map out the dynamical phase diagram for this system, and discuss how our results could be explored in electron liquid crystal systems, type-1.5 superconductors, and pattern-forming colloidal assemblies.

Pinning mode resonances of 2D electron stripe phases: effect of an in-plane magnetic field

We study the anisotropic pinning-mode resonances in the rf conductivity spectra of the stripe phase of 2D electron systems around a Landau level filling of 9/2, in the presence of an in-plane magnetic field B(ip). The polarization along which the resonance is observed switches as B(ip) is applied, consistent with the reorientation of the stripes. The resonance frequency, a measure of the pinning interaction between the 2D electron systems and disorder, increases with B(ip). The magnitude of this increase indicates that disorder interaction is playing an important role in determining the stripe orientation.

Observation of pinning mode of stripe phases of 2D systems in high Landau levels

We study the radio-frequency diagonal conductivities of the anisotropic stripe phases of higher Landau levels near half-integer fillings. In the hard direction, in which larger dc resistivity occurs, the spectrum exhibits a striking resonance, while in the orthogonal, easy direction, no resonance is discernible. The resonance is interpreted as a pinning mode of the stripe phase.