Density-induced interchange of anisotropy axes at half-filled high Landau levels

Hidden Quantum Hall Stripes in Al_{x}Ga_{1-x}As/Al_{0.24}Ga_{0.76}As Quantum Wells

We report on transport signatures of hidden quantum Hall stripe (hQHS) phases in high (N>2) half-filled Landau levels of Al_{x}Ga_{1-x}As/Al_{0.24}Ga_{0.76}As quantum wells with varying Al mole fraction x<10^{-3}. Residing between the conventional stripe phases (lower N) and the isotropic liquid phases (higher N), where resistivity decreases as 1/N, these hQHS phases exhibit isotropic and N-independent resistivity. Using the experimental phase diagram, we establish that the stripe phases are more robust than theoretically predicted, calling for improved theoretical treatment. We also show that, unlike conventional stripe phases, the hQHS phases do not occur in ultrahigh mobility GaAs quantum wells but are likely to be found in other systems.

Anomalous Nematic States in High Half-Filled Landau Levels

It is well established that the ground states of a two-dimensional electron gas with half-filled high (N≥2) Landau levels are compressible charge-ordered states, known as quantum Hall stripe (QHS) phases. The generic features of QHSs are a maximum (minimum) in a longitudinal resistance R_{xx} (R_{yy}) and a nonquantized Hall resistance R_{H}. Here, we report on emergent minima (maxima) in R_{xx} (R_{yy}) and plateaulike features in R_{H} in half-filled N≥3 Landau levels. Remarkably, these unexpected features develop at temperatures considerably lower than the onset temperature of QHSs, suggestive of a new ground state.

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.

Observation of an Anisotropic Wigner Crystal

We report a new correlated phase of two-dimensional charged carriers in high magnetic fields, manifested by an anisotropic insulating behavior at low temperatures. It appears in a large range of low Landau level fillings 1/3≲ν≲2/3 in hole systems confined to wide GaAs quantum wells when the sample is tilted in magnetic field to an intermediate angle. The parallel field component (B_{∥}) leads to a crossing of the lowest two Landau levels, and an elongated hole wave function in the direction of B_{∥}. Under these conditions, the in-plane resistance exhibits an insulating behavior, with the resistance along B_{∥} about 10 times smaller than the resistance perpendicular to B_{∥}. We interpret this anisotropic insulating phase as a two-component, striped Wigner crystal.

The quantum Hall effect at 5/2 filling factor

Experimental discovery of a quantized Hall state at 5/2 filling factor presented an enigmatic finding in an established field of study that has remained an open issue for more than twenty years. In this review we first examine the experimental requirements for observing this state and outline the initial theoretical implications and predictions. We will then follow the chronology of experimental studies over the years and present the theoretical developments as they pertain to experiments, directed at sets of issues. These topics will include theoretical and experimental examination of the spin properties at 5/2; is the state spin polarized? What properties of the higher Landau levels promote development of the 5/2 state, what other correlation effects are observed there, and what are their interactions with the 5/2 state? The 5/2 state is not a robust example of the fractional quantum Hall effect: what experimental and material developments have allowed enhancement of the effect? Theoretical developments from initial pictures have promoted the possibility that 5/2 excitations are exceptional; do they obey non-abelian statistics? The proposed experiments to determine this and their executions in various forms will be presented: this is the heart of this review. Experimental examination of the 5/2 excitations through interference measurements will be reviewed in some detail, focusing on recent results that demonstrate consistency with the picture of non-abelian charges. The implications of this in the more general physics picture is that the 5/2 excitations, shown to be non-abelian, should exhibit the properties of Majorana operators. This will be the topic of the last review section.

Collective modes and the periodicity of quantum Hall stripes

We investigate the quantum Hall stripe phase at filling factor 9/2 at the microscopic level by probing the dispersion of its collective modes with the help of surface acoustic waves with wavelengths down to 60 nm. The dispersion is strongly anisotropic. It is highly dispersive and exhibits a roton minimum for wave vectors aligned along the easy transport direction. In the perpendicular direction, however, the dispersion is featureless, although not flat as predicted by theory. Oscillatory behavior in the absorption intensity of the collective mode with a wave vector perpendicular to the stripes is attributed to a commensurability effect. It allows us to extract the periodicity of the quantum Hall stripes.

Effect of strain on stripe phases in the quantum Hall regime

Preferential orientation of the stripe phases in the quantum Hall (QH) regime has remained a puzzle since its discovery. We show experimentally and theoretically that the direction of high and low resistance of the two-dimensional (2D) hole gas in the QH regime can be controlled by an external strain. Depending on the sign of the in-plane shear strain, the Hartree-Fock energy of holes or electrons is minimized when the charge density wave (CDW) is oriented along the [110] or [110] directions. We suggest that shear strains due to internal electric fields in the growth direction are responsible for the observed orientation of CDW in pristine electron and hole samples.

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.

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

The correlated phases in a two-dimensional electron system with a high index partially filled Landau level are studied in transport under nonequilibrium conditions by imposing a dc-current drive. At filling 1/4 and 3/4 of these Landau levels, where the charge density wave picture predicts an isotropic bubble phase, the dc drive induces anisotropic transport behavior consistent with stripe order. The easy axis of the emerging anisotropic phase is perpendicular to the drive. At half filling the anisotropic stripe phase is stabilized by the dc drive provided drive and easy-axis directions coincide.

Metastable resistance-anisotropy orientation of two-dimensional electrons in high Landau levels

In half-filled high Landau levels, two-dimensional electron systems possess collective phases which exhibit a strongly anisotropic resistivity tensor. A weak, but as yet unknown, rotational symmetry-breaking potential native to the host semiconductor structure is necessary to orient these phases in macroscopic samples. Making use of the known external symmetry-breaking effect of an in-plane magnetic field, we find that the native potential can have two orthogonal local minima. It is possible to initialize the system in the higher minimum and then observe its relaxation toward equilibrium.