TY - JOUR
T1 - Fractional Quantum Hall Effect Energy Gaps
T2 - Role of Electron Layer Thickness
AU - Villegas Rosales, K. A.
AU - Madathil, P. T.
AU - Chung, Y. J.
AU - Pfeiffer, L. N.
AU - West, K. W.
AU - Baldwin, K. W.
AU - Shayegan, M.
N1 - Funding Information:
We acknowledge support by the National Science Foundation (NSF) Grants No. DMR 1709076 and No. DMR 2104771 for measurements. For sample synthesis and characterization, we acknowledge support by NSF Grants No. ECCS 1906253 and No. MRSEC DMR 1420541, and the Gordon and Betty Moore Foundation’s EPiQS Initiative (Grant No. GBMF9615 to L. N. P.). This research is funded in part by QuantEmX Travel Grants from the Institute for Complex Adaptive Matter. A portion of this work was performed at the National High Magnetic Field Laboratory (NHMFL), which is supported by National Science Foundation Cooperative Agreement No. DMR-1644779 and the state of Florida. We thank S. Hannahs, T. Murphy, A. Bangura, G. Jones, and E. Green at NHMFL for technical support. We also thank J. K. Jain for illuminating discussions.
Publisher Copyright:
© 2021 American Physical Society.
PY - 2021/7/30
Y1 - 2021/7/30
N2 - 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.
AB - 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.
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U2 - 10.1103/PhysRevLett.127.056801
DO - 10.1103/PhysRevLett.127.056801
M3 - Article
C2 - 34397247
AN - SCOPUS:85112624046
SN - 0031-9007
VL - 127
JO - Physical review letters
JF - Physical review letters
IS - 5
M1 - 056801
ER -