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

Abstract

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.1 arXiv:1401.3912v1 [cond-mat.mes-hall] 16 Jan 2014In two-dimensional electron systems (2DES) hosted in GaAs an insulating phase occurs at the low Landau filling factor (ν) termination of the fractional quantum Hall effect (FQHE) 1 series. The insulator is understood as a form of Wigner solid 2-14 , a state of matter composed of charge carriers arranged to minimize their mutual repulsion while constrained to a fixed density by charge neutrality. The role of the disorder is crucial in producing the insulating behavior, since the Wigner solid is necessarily pinned by any disorder.The spectra of the low ν insulating phases of 2DES exhibit a microwave or rf resonance 6-9,12,13 that is identified as a pinning mode 7,9,[12][13][14][15] , in which pieces of the solid oscillate collectively about their pinned positions. This disorder-induced mode is a powerful tool for study of solid phases in 2DES, which occur under many conditions 14 besides the low ν insulator. But a detailed understanding of how the solid phase is pinned is lacking.The frequency, f pk , of the resonance has been qualitatively found to increase with increasing accidental disorder, as roughly characterized by the mobilities of a variety of samples, but there is no systematic experimental knowledge of the relationship between the disorder characteristics and the pinning mode, and no microscopic picture of the solid in the presence of disorder.This paper presents pinning mode measurements of the low ν insulator in a series of samples with quantifiable, controlled alloy disorder, produced by using a dilute Al alloy, Al x Ga 1−x As, as the channel in which the 2DES resides. The characteristics of these samples have been well established in earlier work on these wafers [16][17][18][19][20] . In particular, study 16 of the mobility vs x has shown that for x ≤ 0.85% the Al is randomly distributed in the channel, and has allowed modeling the potential around each Al atom as a spherical square well with known radius and potential-depth parameters. Relevant for high magnetic field (B) studies, both this radius and the typical Al spacing in three dimensions are much less than the magnetic length, l B , for all nonzero x that we studied, and for any accessible B. The samples we studied with x > 0 had ∼ 10 2 to 10 3 Al within the typical volume of a carrier.An important aspect of the disorder in 2DES in high B is its effe...

Composite fermion liquid to Wigner solid transition in the lowest Landau level of zinc oxide

“…Such a high resistance phase between ν = 1/3 and 2/7 has also been observed in GaAs, and was interpreted as the electron Wigner solid pinned by disorder. Two mechanisms have been identified for the appearance of the Wigner solid around these filling factors: one is a large LL mixing, which modifies the ground state energies of fractional quantum Hall states and Wigner solid; 4 , 5 , 19 the other is short-range disorder 4 , 27 , 28 . Both mechanisms are more pronounced in ZnO-heterostructures than in GaAs 25 , 29 .…”

Magnetophonons & type-B Goldstones from hydrodynamics to holography

“…As we will see, holography is indeed one of the cases where this does not happen. More interestingly and broadly, the dynamics of the magnetophonon peak as a function of the magnetic field can reveal the fundamental nature of the "disorder" responsible for its pinning [39][40][41][42][43][44][45], and it thus encodes a very valuable insight into the system at hand. In the following section 2, we will provide more details about the physics of magnetophonon resonances.…”

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

“…An explanation 46 of the extended ν range is that in the competition between solid and FQHE liquids, the solid can be more stable in larger disorder due its pinning energy, which the solid gains as carrier positions adjust to the disorder potential. 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.…”

“…The behavior seen for ν < 0.8 is clearly enabled by the disorder, since the disorder extends the resonant range into that region. Disorder stabilizes a solid vs an FQHE liquid since the solid optimizes its energy in the disorder potential, gaining its pinning energy 43 , and the transition to insulator at the low ν termination of the FQHE series occurs around ν = 1/3 in Al alloy-disordered samples 30,35 .…”

“…Samples from the same wafers were used in earlier work in dc transport [32][33][34][35][36] . Characterization 33 of the samples at One sample has x = 0.33%, density n ≈ 2.1 × 10 11 cm −2 and as-cooled mobility µ about 2.3 × 10 6 cm 2 /V-s; the other sample has x = 0.85%, n ≈ 2.5 × 10 11 cm −2 and µ ≈ 1.4 × 10 6 cm 2 /V-s. A previous paper 37 showed that samples from this series exhibit pinning mode resonances at the low ν termination of the FQHE series, which for these disordered samples occurred for ν below that of the 1/3 FQHE. The presence of disorder is known 16 to raise the ν at which the FQHE series is terminated in an insulator.…”