arXiv subjects

L. W. Engel

Publications and source records attributed to L. W. Engel.

At least 19 recordsLinked to original sources

arXiv2024

Two-dimensional hydrodynamic viscous electron flow in annular Corbino rings

The concept of fluidic viscosity is ubiquitous in our everyday life and for it to arise the fluidic medium must necessarily form a continuum where macroscopic properties can emerge. While a powerful concept for tangible liquids, hydrodynamic manifestation of collective flow in electronic systems such as two-dimensional electron gases (2DEGs) has only been shown recently to occur in graphene and GaAs/AlGaAs. Here, we present nonlocal electronic transport measurements in concentric annular rings formed in high-mobility GaAs/AlGaAs 2DEGs and the resulting data strongly suggest that viscous hydrodynamic flow can occur far away from the source-drain current region. Our conclusion of viscous electronic transport is further corroborated by simulations of the Navier-Stokes equations that are found to be in agreement with our measurements below 1K temperature. Most importantly, our work emphasizes the key role played by viscosity via electron-electron (e-e) interaction when hydrodynamic transport is restricted radially, and for which a priori should not have played a major role.

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arXiv2024

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 last 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 $\simeq$35 MHz. The amount of reduction of \fp\ 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.

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arXiv2024

Signatures of correlated defects in an ultra-clean 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, ultra-high-purity, two-dimensional electrons confined to GaAs quantum wells. The WC domains in these samples contain $\simeq$ 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, hyper-corelated 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.

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arXiv2024

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 non-linear current-voltage (\textit{I-V}) and noise characteristics. We report here, measurements on an ultra-low-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 non-linear \textit{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.

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arXiv2022

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 ($ν\lesssim1/6$) has long been a topic of interest and controversy in condensed matter. Following the recent breakthrough in the quality of ultra-high-mobility GaAs 2DESs, we revisit this problem experimentally and investigate the impact of reduced disorder. In a GaAs 2DES sample with density $n=6.1\times10^{10}$ /cm$^2$ and mobility $μ=25\times10^6$ cm$^2$/Vs, we find a deep minimum in the longitudinal magnetoresistance ($R_{xx}$) at $ν=1/7$ when $T\simeq104$ mK. There is also a clear sign of a developing minimum in the $R_{xx}$ at $ν=2/13$. While insulating phases are still predominant when $ν\lesssim1/6$, these minima strongly suggest the existence of fractional quantum Hall states at filling factors that comply with the Jain sequence $ν=p/(2mp\pm1)$ even in the very low Landau level filling limit. The magnetic field dependent activation energies deduced from the relation $R_{xx}\propto e^{E_A/2kT}$ corroborate this view, and imply the presence of pinned Wigner solid states when $ν\neq p/(2mp\pm1)$. Similar results are seen in another sample with a lower density, further generalizing our observations.

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arXiv2022

Resistively loaded coplanar waveguide for microwave measurements of induced carriers

We describe the use of a coplanar waveguide whose slots are filled with resistive film, a resistively loaded coplanar waveguide (RLCPW), to measure two dimensional electron systems (2DES). The RLCPW applied to the sample hosting the 2DES provides a uniform metallic surface serving as a gate, to control the areal charge density of the 2DES. As a demonstration of this technique we present measurements on a Si MOSFET, and a model that successfully converts microwave transmission coefficients into conductivity of a nearby 2DES capacitively coupled to the RLCPW. We also describe the process of fabricating the highly resistive metal film required for fabrication of the RLCPW.

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arXiv2019

Probing the Melting of a Two-dimensional Quantum Wigner Crystal via its Screening Efficiency

One of the most fundamental and yet elusive collective phases of an interacting electron system is the quantum Wigner crystal (WC), an ordered array of electrons expected to form when the electrons' Coulomb repulsion energy eclipses their kinetic (Fermi) energy. In low-disorder, two-dimensional (2D) electron systems, the quantum WC is known to be favored at very low temperatures ($T$) and small Landau level filling factors ($ν$), near the termination of the fractional quantum Hall states. This WC phase exhibits an insulating behavior, reflecting its pinning by the small but finite disorder potential. An experimental determination of a $T$ vs $ν$ phase diagram for the melting of the WC, however, has proved to be challenging. Here we use capacitance measurements to probe the 2D WC through its effective screening as a function of $T$ and $ν$. We find that, as expected, the screening efficiency of the pinned WC is very poor at very low $T$ and improves at higher $T$ once the WC melts. Surprisingly, however, rather than monotonically changing with increasing $T$, the screening efficiency shows a well-defined maximum at a $T$ which is close to the previously-reported melting temperature of the WC. Our experimental results suggest a new method to map out a $T$ vs $ν$ phase diagram of the magnetic-field-induced WC precisely.

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arXiv2018

Wigner solids of wide quantum wells near Landau filling $ν=1$

Microwave spectroscopy within the Landau filling ($ν$) range of the integer quantum Hall effect (IQHE) has revealed pinning mode resonances signifying Wigner solids (WSs) composed of quasi-particles or -holes. We study pinning modes of WSs in wide quantum wells (WQWs) for $ 0.8\leν\le1.2$, varying the density, $n$, and tilting the sample by angle $θ$ in the magnetic field. Three distinct WS phases are accessed. One phase, S1, is phenomenologically the same as the WS observed in the IQHEs of narrow QWs. The second phase, S2, exists at $ν$ further from $ν=1$ than S1, and requires a sufficiently large $n$ or $θ$, implying S2 is stabilized by the Zeeman energy. The melting temperatures of S1 and S2, estimated from the disappearance of the pinning mode, show different behavior vs $ν$. At the largest $n$ or $θ$, S2 disappears and the third phase, S1A, replaces S1, also exhibiting a pinning mode. This occurs as the WQW $ν=1$ IQHE becomes a two-component, Halperin-Laughlin $\pone$ state. We interpret S1A as a WS of the excitations of $\pone$, which has not been previously observed.

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arXiv2018

Wigner solid pinning modes tuned by fractional quantum Hall states of a nearby layer

We study a bilayer system hosting exotic many-body states of two-dimensional electron systems (2DESs) in close proximity but isolated from one another by a thin barrier. One 2DES has low electron density and forms a Wigner solid (WS) at high magnetic fields. The other has much higher density and, in the same field exhibits fractional quantum Hall states (FQHSs). The WS manifests microwave resonances which are understood as pinning modes, collective oscillations of the WS within the small but finite ubiquitous disorder. Our measurements reveal a striking evolution of the pinning mode frequencies of the WS layer with the formation of the FQHSs in the nearby layer, evincing a strong coupling between the WS pinning modes and the state of the 2DES in the adjacent layer, mediated by screening.

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arXiv2018

Critical Filling Factor for the Formation of a Quantum Wigner Crystal Screened by a Nearby Layer

One of the most fascinating ground states of an interacting electron system is the so-called Wigner crystal where the electrons, in order to minimize their repulsive Coulomb energy, form an ordered array. Here we report measurements of the critical filling factor ($ν_{C}$) below which a magnetic-field-induced, quantum Wigner crystal forms in a dilute, two-dimensional electron layer when a second, high-density electron layer is present in close proximity. The data reveal that the Wigner crystal forms at a significantly smaller $ν_{C}$ compared to the $ν_{C}$ ($\simeq 0.20$) in single-layer two-dimensional electron systems. The measured $ν_{C}$ exhibits a strong dependence on the interlayer distance, reflecting the interaction and screening from the adjacent, high-density layer.

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arXiv2016

Microwave spectroscopic observation of a Wigner solid within the 1/2 fractional quantum Hall effect

The fractional quantum Hall effect (FQHE) states at half integer Landau fillings ($ν$) have long been of great interest, since they have correlations that differ from those of the fundamental Laughlin states found at odd denominators. At $ν=1/2$ the FQHE has been observed in wide or double quantum wells, and is ascribed to the two-component Halperin-Laughlin $Ψ_{331}$ state. $Ψ_{331}$ excitations carry charge $\pm e/4$, like the carriers of $ν=5/2$ states which are of interest in quantum computation. Further, such an excitation (quasiparticle or -hole) of $Ψ_{331}$ has unequal, opposite charge in the top and bottom layers, and hence an up or down dipole moment. Here we report evidence for a Wigner solid (WS) of such dipolar quasiholes from a quantitative study of the microwave spectra of a wide quantum well (WQW) at $ν$ close to 1/2.

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arXiv2014

Microwave pinning modes near Landau filling $ν=1$ in two-dimensional electron systems with alloy disorder

We report measurements of microwave spectra of two-dimensional electron systems hosted in dilute Al alloy, Al$_x$Ga$_{1-x}$As, for a range of Landau level fillings, $ν$, around 1. For $ν>0.8$ or $ν<1.2$, the samples exhibit a microwave resonance whose frequency decreases as $ν$ moves away from 1. A resonance with this behavior is the signature of solids of quasiparticles or -holes in the partially occupied Landau level, which was previously seen in ultralow disorder samples. For $ν<0.8$ down to as low as $ν=0.54$, a resonance in the spectra is still present in the Al alloy-disordered samples, though it is partially or completely suppressed at $ν=3/5$ and $1/2$, and is strongly damped over much of this $ν$ range. The resonance also shows a striking enhancement in peak frequency for $ν$ just below 3/4. We discuss possible explanations of the resonance behavior for $ν<0.8$ in terms of the composite fermion picture.

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arXiv2014

Microwave spectroscopic studies of the bilayer electron solid states at low Landau filling in a wide quantum well

At the low Landau filling factor $(ν)$ termination of the fractional quantum Hall effect (FQHE) series, two-dimensional electron systems (2DESs) exhibit an insulating phase that is understood as a form of pinned Wigner solid. Here we use microwave spectroscopy to probe the transition to the insulator for a wide quantum well (WQW) sample that can support single-layer or bilayer states depending on its overall carrier density, $n$. We find the insulator exhibits a resonance, which is characteristic of a bilayer solid. The resonance also reveals a pair of transitions within the solid, which are not accessible to dc transport measurements. As $n$ is biased deeper into the bilayer solid regime, the resonance grows in specific intensity, and the transitions within the insulator disappear. These behaviors are suggestive of a picture of the insulating phase as an emulsion of liquid and solid components.

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arXiv2014

Multiphoton processes at cyclotron resonance subharmonics in a 2D electron system under DC and microwave excitation

We investigate a two-dimensional electron system (2DES) under microwave illumination at cyclotron resonance subharmonics. The 2DES carries sufficient direct current, $I$, that the differential resistivity oscillates as $I$ is swept. At magnetic fields sufficient to resolve individual Landau levels, we find the number of oscillations within an $I$ range systematically changes with increasing microwave power. Microwave absorption and emission of $N$ photons, where $N$ is controlled by the microwave power, describes our observations in the framework of the displacement mechanism of impurity scattering between Hall-field tilted Landau levels.

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arXiv2014

Pinning modes of high magnetic field Wigner solids with controlled alloy disorder

For a series of samples with 2D electron systems in dilute Al_x Ga_{1-x}As, with varying x from 0 to 0.8 %, we survey the pinning mode resonances of Wigner solids at the low Landau filling termination of the fractional quantum Hall effect (FQHE) series. For all x studied, the pinning modes are present with frequencies, f_pk, that are consistent with collective weak pinning. For x>=0.22% we find f_pk vs B exhibits a rapid increase that is not present for x=0. We find the observed f_pk is much smaller than values calculated with a simple Wigner solid model which neglects the effects of the disorder on the charge distribution of a carrier.

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arXiv2013

Microwave spectroscopic observation of distinct electron solid phases in wide quantum wells

In high magnetic fields ($B$), two dimensional electron systems (2DESs) can form a number of phases in which interelectron repulsion plays the central role, since the kinetic energy is frozen out by Landau quantization. These phases include the well-known liquids of the fractional quantum Hall effect (FQHE), as well as solid phases with broken spatial symmetry and crystalline order. Solids can occur at the low Landau filling ($ν$) termination of the FQHE series, but also within integer quantum Hall effects (IQHEs). Here, we present microwave spectroscopy studies of wide quantum wells (WQWs). The spectra clearly reveal two distinct solid phases, hidden within what in dc transport would be the zero diagonal conductivity of an integer quantum Hall effect state. Explanation of these solids is not possible with the simple picture of a Wigner solid (WS) of ordinary (quasi) electrons or holes.

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arXiv2012

Resistivity saturation in a weakly interacting 2D Fermi liquid at intermediate temperatures

We report a highly unusual temperature dependence in the magnetoresistance of a weakly interacting high mobility 2D electron gas (2DEG) under a parallel magnetic field and when the current is perpendicular to the field. While the linear temperature dependence below 10 K and the exponential temperature dependence above 40 K agree with existing theory of electron-phonon scattering, a field induced resistivity saturation behaviour characterized by an almost complete suppression of the temperature dependence is observed from approximately 20 to 40 K, which is in sharp contrast to the phenomenology observed when the current is parallel to the field. Possible origins of this intriguing intermediate temperature phenomenon are discussed.

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arXiv2011

Unequal Layer Densities in Bilayer Wigner Crystal at High Magnetic Field

We report studies of pinning mode resonances of magnetic field induced bilayer Wigner crystals of bilayer hole samples with negligible interlayer tunneling and different interlayer separations d, in states with varying layer densities, including unequal layer densities. With unequal layer densities, samples with large d relative to the in-plane carrier-carrier spacing a, two pinning resonances are present, one for each layer. For small d/a samples, a single resonance is observed even with significant density imbalance. These samples, at balance, were shown to exhibit an enhanced pinning mode frequency [Zhihai Wang et al., Phys. Rev. Lett. 136804 (2007)], which was ascribed to a one-component, pseudospin ferromagnetic Wigner solid. The evolution of the resonance frequency and line width indicates the quantum interlayer coherence survives at moderate density imbalance, but disappears when imbalance is sufficiently large.

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