At low Landau level filling factors ($\nu$), Wigner solid phases of two-dimensional electron systems in GaAs are pinned by disorder and exhibit a pinning mode, whose frequency is a measure of the disorder that pins the Wigner solid. Despite numerous studies spanning the past three decades, the origin of the disorder that causes the pinning and determines the pinning mode frequency remains unknown. Here, we present a study of the pinning mode resonance in the low-$\nu$ Wigner solid phases of a series of ultralow-disorder GaAs quantum wells which are similar except for their varying well widths $d$. The pinning mode frequencies $f_p$ decrease strongly as $d$ increases, with the widest well exhibiting $f_p$ as low as $\simeq 35\mathrm{MHz}$. The amount of reduction of $f_p$ with increasing $d$ can be explained remarkably well by tails of the wave function impinging into the alloy-disordered ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ barriers that contain the electrons. However, it is imperative that the model for the confinement and wave function includes the Coulomb repulsion in the growth direction between the electrons as they occupy the quantum well.

中文翻译：

---

磁场诱导维格纳固体中钉扎无序的起源

在低朗道水平填充因子（$\nu$），GaAs 中二维电子系统的维格纳固相被无序钉扎并表现出钉扎模式，其频率是钉扎维格纳固体的无序程度的度量。尽管过去三十年进行了大量研究，但引起钉扎并决定钉扎模式频率的紊乱的起源仍然未知。在这里，我们提出了低钉扎模式共振的研究$\nu$一系列超低无序 GaAs 量子阱的维格纳固相，除了不同的阱宽度外，它们相似$d$。钉扎模式频率$F_p$强烈减少为$d$增加，最广泛的油井表现出$F_p$低至$\simeq 35\mathrm{兆赫兹}$。减少金额为$F_p$随着增加$d$可以通过波函数的尾部撞击合金无序结构来很好地解释${铝}_X{嘎}_{1-X}\mathrm{作为}$包含电子的势垒。然而，当电子占据量子阱时，约束和波函数的模型必须包括电子之间生长方向上的库仑斥力。