Melting of a 2D quantum electron solid in high magnetic field

Chen, Yong P.; Sambandamurthy, G.; Wang, Z. H.; Lewis, Rupert; Engel, L. W.; Tsui, D. C.; Ye, P. D.; Pfeiffer, L. N.; West, K. W.

doi:10.1038/nphys322

Cited by 86 publications

(87 citation statements)

References 34 publications

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“…A system of 29 particles has three stable configurations which are, in the order of increasing energy: (4, 10, 15), (5,10,14), and (4,11,14). As one can see from the corresponding graph, in the high-temperature limit the probabilities of all three states are of comparable magnitude.…”

Section: Resultsmentioning

confidence: 48%

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Metastable configurations of Wigner crystals in a circular trap

Anisimovas¹,

Rancova²,

Varanavičius³

2010

Lithuanian J. Phys.

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We model the formation of ordered structures in systems consisting of up to 52 identical particles interacting by Coulomb repulsion forces and confined within a two-dimensional parabolic trap. Our algorithm consists of a number of Metropolis steps followed by the steepest-descent minimization of the total potential energy of the system. The role of the first (Metropolis) stage is to create a random canonically distributed configuration, while the subsequent minimization locates the closest local minimum starting from this random configuration. In most cases we find that more than one stable configuration may be formed, and often the lowest-energy configuration is not the most probable one. The concept of configurational entropy is introduced to quantify the uncertainty due to the availability of several alternative structures.

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Section: Resultsmentioning

confidence: 48%

“…As a matter of fact, the formation of a threedimensional lattice of electrons was never realized, however, its two-dimensional analogue turns out to be feasible in electron systems confined on the surface of liquid helium [1,8] as well as in semiconductor heterostructures [9,10].…”

Section: Introductionmentioning

confidence: 99%

Metastable configurations of Wigner crystals in a circular trap

Anisimovas¹,

Rancova²,

Varanavičius³

2010

Lithuanian J. Phys.

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“…A possible explanation of the discrepancy lies in the increased pinning experienced by the FMBWC, since the pinning energy can stabilize the FMBWC against the more weakly pinned AFMBWC phases that succeed it at largerd. It is likely that pinning energy plays a role in stabilizing single layer Wigner crystals against the FQHE liquid at high fillings [29], and against melting at elevated temperatures [16]. A possible clue to the presently estimatedd * ≈ 1.8 is that it is close to the maximald values below which the interlayer correlated QH states at ν = 1 and 1/2 exist, respectivelỹ d ≈ 1.8 [1,3] and 2 [4].…”

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confidence: 99%

“…Pinning also produces a striking microwave or rf conductivity resonance, or "pinning mode", which is a collective oscillation of the carriers about their pinned positions. Pinning mode resonances of single layers have been studied experimentally [15,16,17,18,19,20] and theoretically [21,22,23] and have proven to be valuable for obtaining information about single layer, pinned Wigner solids. The resonance frequency always increases as the disorder strength increases, and is also sensitive [21,22,23] to the correlation length of the effective disorder, which takes into account the spread of the carrier wave functions.…”

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confidence: 99%

Pinning Modes and Interlayer Correlation in High-Magnetic-Field Bilayer Wigner Solids

et al. 2007

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We report studies of pinning mode resonances in the low total Landau filling (ν) Wigner solid of a series of bilayer hole samples with negligible interlayer tunneling, and with varying interlayer separation d. Comparison of states with equal layer densities (p, p) to single layer states (p, 0) produced in situ by biasing, indicates that there is interlayer quantum correlation in the solid at small d. Also, the resonance frequency at small d is decreased just near ν = 1/2 and 2/3, indicating the importance in the solid of correlations related to those in the fractional quantum Hall effects.Bilayers, closely spaced sheets of carriers in semiconductor hosts, exhibit phenomena that arise from interlayer interaction and quantum correlation and so are not present in single layers. Of particular importance is the the quantum Hall (QH) state at total bilayer Landau filling factor ν = 1, for the case of small interlayer separation and weak interlayer tunneling. Owing to striking phenomena, both in magnetotransport [1,2] and in interlayer tunneling [3], that state is understood to have carrier wave functions which extend coherently between the two layers, with the difference in the quantum phase between the layers spontaneously developing long range spatial coherence over the plane. This ν = 1 state can be thought of as bilayer exciton condensate, excitonic counterflow superfluid, or a pseudospin ferromagnet with magnetization in the plane. As usual in describing bilayer states, pseudospin specifies the layer.Interlayer quantum correlation, in the sense of wave functions spreading coherently between layers when tunneling is small, is present in bilayers at other ν than one. Such interlayer correlation underlies the ν = 1/2 [4, 5, 6] and 3/2 [6,7] fractional QH effects (FQHE) observed in bilayers. This work will focus on interlayer correlation within bilayer Wigner crystal (BWC) phases [8,9,10], in samples with negligible interlayer tunneling. Wigner crystals, lattices stabilized by repulsion between carriers, have been predicted in the absence of disorder [11,12] for bilayers, as well as for single layer systems [13], at the low ν termination of the QH series.Theories [11,12,14] have predicted a number of distinct BWC phases. The relative importance of interlayer and intralayer interaction is crucial in these theories, and is measured by the ratio d/a, where d is the center-tocenter layer separation, a = (2πp) −1/2 is the mean inplane carrier spacing and p is the carrier density per layer. A one component triangular lattice is expected at small enough d/a, and is an easy plane pseudospin ferromagnetic BWC (FMBWC) with one carrier, evenly and coherently spread between the two layers, at each lattice site. Interlayer-staggered two component lattices occur at larger d/a, and without interlayer tunneling, are pseudospin antiferromagnetic BWCs (AFMBWC), with carriers essentially completely in one layer alternating with those completely in the other. Multiple staggered two component phases are predicted, including square and ...

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“…This is also the explanation for the transition to insulator at the low ν termination of the FQHE series occurring around ν = 1/3 in Al alloy-disordered samples 32,37 (as opposed to near 1/5 in ultralow disorder samples 8 ). The resonance also sets in as ν goes below 1/3 in low-density samples 47 or in which the pinning energy is presumably more important relative to the carrier interaction.…”

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confidence: 99%

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

et al. 2015

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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 alloydisordered 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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Melting of a 2D quantum electron solid in high magnetic field

Cited by 86 publications

References 34 publications

Metastable configurations of Wigner crystals in a circular trap

Metastable configurations of Wigner crystals in a circular trap

Pinning Modes and Interlayer Correlation in High-Magnetic-Field Bilayer Wigner Solids

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

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