Fractional quantum Hall effect energy gap: role of electron layer thickness

Abstract

The fractional quantum Hall effect (FQHE) stands as a quintessential manifestation of an interacting two-dimensional electron system. One of FQHE'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 quantitative comparison between the measured energy gaps and the available theoretical calculations that take into account the role of finite layer thickness and Landau level mixing. Our systematic experimental study of the FQHE energy gaps uses very high-quality two-dimensional electron systems confined to GaAs quantum wells with varying well widths. All the measured energy gaps fall bellow 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 the measured energy gaps to be in reasonable quantitative agreement with calculations, although some discrepancies remain.

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• Non-Abelian Anyons and Topological Quantum Computation
• Fractional statistics in anyon collisions
• Aharonov-Bohm interference of fractional quantum Hall edge modes
• Working principles of doping-well structures for high-mobility two-dimensional electron systems
• Microwave spectroscopic studies of the bilayer electron solid states at low Landau filling in a wide quantum well
• Interplay between Quantum Well Width and Interface Roughness for Electron Transport Mobility in GaAs Quantum Wells

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