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.

中文翻译：

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分数量子霍尔效应能隙：电子层厚度的作用

分数量子霍尔效应是相互作用的二维电子系统的典型表现。分数量子霍尔效应最基本的特征之一是将不可压缩的基态与其激发分开的能隙。然而，尽管进行了近四年的研究，理论计算的能隙和实验测量的能隙之间缺乏定量一致。在这里，我们报告了一项系统的实验研究，该研究将非常高质量的二维电子系统限制在具有固定密度和不同阱宽的 GaAs 量子阱中。结果表明，随着电子层变厚和库仑相互作用的短程分量减弱，能隙明显减小。我们还提供了测量的能隙与考虑到有限层厚度和朗道级混合作用的可用理论计算之间的定量比较。所有测量的能隙都低于计算值，但随着电子层厚度的增加，实验和计算的结果越来越接近。以现象学的方式解释无序的作用，我们发现测量的能隙和计算的能隙之间具有更好的整体一致性，尽管仍然存在一些令人费解的差异。实验和计算的结果越来越接近。以现象学的方式解释无序的作用，我们发现测量的能隙和计算的能隙之间具有更好的整体一致性，尽管仍然存在一些令人费解的差异。实验和计算的结果越来越接近。以现象学的方式解释无序的作用，我们发现测量的能隙和计算的能隙之间具有更好的整体一致性，尽管仍然存在一些令人费解的差异。