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

Rosales, K. A. Villegas; Madathil, P. T.; Chung, Yoon Jang; Pfeiffer, L. N.; West, K. W.; Baldwin, K. W.; Shayegan, M.

doi:10.1103/physrevlett.127.056801

Cited by 17 publications

(25 citation statements)

References 42 publications

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“…[8] and the red squares are obtained from a linear fit of the experimental data at ν = 1/3, 2/5, 3/7 in Ref. [8]. quantum well width.…”

Section: Resultsmentioning

confidence: 99%

“…In the following calculations, we set κ = 0.70 and 0.76 at ν = 1/3 and 2/5, respectively, as appropriate for the experiments of Ref. [8], with electron density ρ = 1.1×10 11 cm −2 .…”

Section: Llm: Perturbative Approachmentioning

confidence: 99%

“…A recent article by Villegas Rosales et al has reported on systematic measurements of the gaps and their quantum well width dependence in the highest mobility samples available to date [8]. The modest aim of our work below is to determine the theoretical values of gaps incorporating, to the best extent we currently know, the effects of finite width and LL mixing (LLM), hoping to gain a better quantitative understanding of this important issue.…”

Section: Introductionmentioning

confidence: 97%

“…It has been appreciated since the very beginning that the existence of a gap is a fundamental property of a fractional quantum Hall effect (FQHE) state [1,2]. Despite the passage of almost four decades, the quantitative agreement between the experimentally measured [3][4][5][6][7][8] and the theoretically predicted [9][10][11][12][13][14][15][16][17][18] values of the gaps is not as good as one might have hoped. In the idealized limit where electrons are in a strict two-dimensional (2D) layer and Landau level (LL) mixing and disorder are absent, comparisons with computer calculations show that the zeroth-order composite fermion (CF) theory predicts gaps of the n/(2n ± 1) FQHE states to within 10%, and the agreement can be further improved by allowing for CF-LL mixing [9,19].…”

Section: Introductionmentioning

confidence: 99%

“…Park et al [14] evaluated gaps for fractions along the n/(2n + 1) sequence with a variational Monte Carlo (VMC) method using wave functions from the CF theory, treating finite width in a LDA; they did not go to large widths that have been studied in Ref. [8]. Morf et al [16] evaluated gaps by performing exact diagonalization (ED); they used a Gaussian model for the transverse wave function to simulate the LDA wave function.…”

Section: Introductionmentioning

confidence: 99%

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Revisiting excitation gaps in the fractional quantum Hall effect

Zhao,

Kudo,

Faugno

et al. 2022

Preprint

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Recent systematic measurements of the quantum well width dependence of the excitation gaps of fractional quantum Hall states in high mobility samples [Villegas Rosales et al., Phys. Rev. Lett. 127, 056801 (2021)] open the possibility of a better quantitative understanding of this important issue. We present what we believe to be accurate theoretical gaps including the effects of finite width and Landau level (LL) mixing. While theory captures the width dependence, there still remains a deviation between the calculated and the measured gaps, presumably caused by disorder. It is customary to model the experimental gaps of the n/(2n±1) states as ∆ n/(2n±1) = Ce 2 /[(2n±1)εl]− Γ, where ε is the dielectric constant of the background semiconductor and l is the magnetic length; the first term is interpreted as the cyclotron energy of composite fermions and Γ as a disorderinduced broadening of composite-fermion LLs. Fitting the gaps for various fractional quantum Hall states, we find that Γ can be nonzero even in the absence of disorder.

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“…[8] and the red squares are obtained from a linear fit of the experimental data at ν = 1/3, 2/5, 3/7 in Ref. [8]. quantum well width.…”

Section: Resultsmentioning

confidence: 99%

“…In the following calculations, we set κ = 0.70 and 0.76 at ν = 1/3 and 2/5, respectively, as appropriate for the experiments of Ref. [8], with electron density ρ = 1.1×10 11 cm −2 .…”

Section: Llm: Perturbative Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%