Origin of Pinning Disorder in Magnetic-Field-Induced Wigner Solids.

At low Landau level filling factors (ν), Wigner solid phases of two-dimensional electron systems in GaAs are pinned by disorder and exhibit a pinning mode, whose frequency is a measure of the disorder that pins the Wigner solid. Despite numerous studies spanning the past three decades, the origin of the disorder that causes the pinning and determines the pinning mode frequency remains unknown. Here, we present a study of the pinning mode resonance in the low-ν Wigner solid phases of a series of ultralow-disorder GaAs quantum wells which are similar except for their varying well widths d. The pinning mode frequencies f_{p} decrease strongly as d increases, with the widest well exhibiting f_{p} as low as ≃35 MHz. The amount of reduction of f_{p} with increasing d can be explained remarkably well by tails of the wave function impinging into the alloy-disordered Al_{x}Ga_{1-x}As barriers that contain the electrons. However, it is imperative that the model for the confinement and wave function includes the Coulomb repulsion in the growth direction between the electrons as they occupy the quantum well.

Signatures of Correlated Defects in an Ultraclean Wigner Crystal in the Extreme Quantum Limit.

Low-disorder two-dimensional electron systems in the presence of a strong, perpendicular magnetic field terminate at very small Landau level filling factors in a Wigner crystal (WC), where the electrons form an ordered array to minimize the Coulomb repulsion. The nature of this exotic, many-body, quantum phase is yet to be fully understood and experimentally revealed. Here we probe one of WC's most fundamental parameters, namely, the energy gap that determines its low-temperature conductivity, in record mobility, ultrahigh-purity, two-dimensional electrons confined to GaAs quantum wells. The WC domains in these samples contain ≃1000 electrons. The measured gaps are a factor of three larger than previously reported for lower quality samples, and agree remarkably well with values predicted for the lowest-energy, intrinsic, hypercorrelated bubble defects in a WC made of flux-electron composite fermions, rather than bare electrons. The agreement is particularly noteworthy, given that the calculations are done for disorder-free composite fermion WCs, and there are no adjustable parameters. The results reflect the exceptionally high quality of the samples, and suggest that composite fermion WCs are indeed more stable compared to their electron counterparts.

Moving Crystal Phases of a Quantum Wigner Solid in an Ultra-High-Quality 2D Electron System.

In low-disorder, two-dimensional electron systems (2DESs), the fractional quantum Hall states at very small Landau level fillings (ν) terminate in a Wigner solid (WS) phase, where electrons arrange themselves in a periodic array. The WS is typically pinned by the residual disorder sites and manifests an insulating behavior, with nonlinear current-voltage (I-V) and noise characteristics. We report here measurements on an ultralow-disorder, dilute 2DES, confined to a GaAs quantum well. In the ν<1/5 range, superimposed on a highly insulating longitudinal resistance, the 2DES exhibits a developing fractional quantum Hall state at ν=1/7, attesting to its exceptional high quality and dominance of electron-electron interaction in the low filling regime. In the nearby insulating phases, we observe remarkable nonlinear I-V and noise characteristics as a function of increasing current, with current thresholds delineating three distinct phases of the WS: a pinned phase (P1) with very small noise, a second phase (P2) in which dV/dI fluctuates between positive and negative values and is accompanied by very high noise, and a third phase (P3) where dV/dI is nearly constant and small, and noise is about an order of magnitude lower than in P2. In the depinned (P2 and P3) phases, the noise spectrum also reveals well-defined peaks at frequencies that vary linearly with the applied current, suggestive of washboard frequencies. We discuss the data in light of a recent theory that proposes different dynamic phases for a driven WS.

Delocalization and Universality of the Fractional Quantum Hall Plateau-to-Plateau Transitions.

Disorder and electron-electron interaction play essential roles in the physics of electron systems in condensed matter. In two-dimensional, quantum Hall systems, extensive studies of disorder-induced localization have led to the emergence of a scaling picture with a single extended state, characterized by a power-law divergence of the localization length in the zero-temperature limit. Experimentally, scaling has been investigated via measuring the temperature dependence of plateau-to-plateau transitions between the integer quantum Hall states (IQHSs), yielding a critical exponent κ≃0.42. Here we report scaling measurements in the fractional quantum Hall state (FQHS) regime where interaction plays a dominant role. Our Letter is partly motivated by recent calculations, based on the composite fermion theory, that suggest identical critical exponents in both IQHS and FQHS cases to the extent that the interaction between composite fermions is negligible. The samples used in our experiments are two-dimensional electron systems confined to GaAs quantum wells of exceptionally high quality. We find that κ varies for transitions between different FQHSs observed on the flanks of Landau level filling factor ν=1/2 and has a value close to that reported for the IQHS transitions only for a limited number of transitions between high-order FQHSs with intermediate strength. We discuss possible origins of the nonuniversal κ observed in our experiments.

Fractional Quantum Hall State at Filling Factor ν=1/4 in Ultra-High-Quality GaAs Two-Dimensional Hole Systems.

Single-component fractional quantum Hall states (FQHSs) at even-denominator filling factors may host non-Abelian quasiparticles that are considered to be building blocks of topological quantum computers. Such states, however, are rarely observed in the lowest-energy Landau level, namely at filling factors ν<1. Here, we report evidence for an even-denominator FQHS at ν=1/4 in ultra-high-quality two-dimensional hole systems confined to modulation-doped GaAs quantum wells. We observe a deep minimum in the longitudinal resistance at ν=1/4, superimposed on a highly insulating background, suggesting a close competition between the ν=1/4 FQHS and the magnetic-field-induced, pinned Wigner solid states. Our experimental observations are consistent with the very recent theoretical calculations that predict that substantial Landau level mixing, caused by the large hole effective mass, can induce composite fermion pairing and lead to a non-Abelian FQHS at ν=1/4. Our results demonstrate that Landau level mixing can provide a very potent means for tuning the interaction between composite fermions and creating new non-Abelian FQHSs.

Correlated States of 2D Electrons near the Landau Level Filling ν=1/7.

The ground state of two-dimensional electron systems (2DESs) at low Landau level filling factors (ν≲1/6) has long been a topic of interest and controversy in condensed matter. Following the recent breakthrough in the quality of ultrahigh-mobility GaAs 2DESs, we revisit this problem experimentally and investigate the impact of reduced disorder. In a GaAs 2DES sample with density n=6.1×10^{10}/cm^{2} and mobility µ=25×10^{6} cm^{2}/V s, we find a deep minimum in the longitudinal magnetoresistance (R_{xx}) at ν=1/7 when T≃104 mK. There is also a clear sign of a developing minimum in R_{xx} at ν=2/13. While insulating phases are still predominant when ν≲1/6, these minima strongly suggest the existence of fractional quantum Hall states at filling factors that comply with the Jain sequence ν=p/(2mp±1) even in the very low Landau level filling limit. The magnetic-field-dependent activation energies deduced from the relation R_{xx}∝e^{E_{A}/2kT} corroborate this view and imply the presence of pinned Wigner solid states when ν≠p/(2mp±1). Similar results are seen in another sample with a lower density, further generalizing our observations.

Fractional Quantum Hall Effect Energy Gaps: Role of Electron Layer Thickness.

The fractional quantum Hall effect stands as a quintessential manifestation of an interacting two-dimensional electron system. One of the fractional quantum Hall effect's most fundamental characteristics is the energy gap separating the incompressible ground state from its excitations. Yet, despite nearly four decades of investigations, a quantitative agreement between the theoretically calculated and experimentally measured energy gaps is lacking. Here we report a systematic experimental study that incorporates very high-quality two-dimensional electron systems confined to GaAs quantum wells with fixed density and varying well widths. The results demonstrate a clear decrease of the energy gap as the electron layer is made thicker and the short-range component of the Coulomb interaction is weakened. We also provide a quantitative comparison between the measured energy gaps and the available theoretical calculations that takes into account the role of finite layer thickness and Landau level mixing. All the measured energy gaps fall below the calculations, but as the electron layer thickness increases, the results of experiments and calculations come closer. Accounting for the role of disorder in a phenomenological manner, we find better overall agreement between the measured and calculated energy gaps, although some puzzling discrepancies remain.

Ultra-high-quality two-dimensional electron systems.

Two-dimensional electrons confined to GaAs quantum wells are hallmark platforms for probing electron-electron interactions. Many key observations have been made in these systems as sample quality has improved over the years. Here, we present a breakthrough in sample quality via source-material purification and innovation in GaAs molecular beam epitaxy vacuum chamber design. Our samples display an ultra-high mobility of 44 × 106 cm2 V-1 s-1 at an electron density of 2.0 × 1011 cm-2. These results imply only 1 residual impurity for every 1010 Ga/As atoms. The impact of such low impurity concentration is manifold. Robust stripe and bubble phases are observed, and several new fractional quantum Hall states emerge. Furthermore, the activation gap (Δ) of the fractional quantum Hall state at the Landau-level filling (ν) = 5/2, which is widely believed to be non-Abelian and of potential use for topological quantum computing, reaches Δ ≈ 820 mK. We expect that our results will stimulate further research on interaction-driven physics in a two-dimensional setting and substantially advance the field.