Wigner solid or Anderson solid -- 2D electrons in strong disorder

Abstract

Critically analyzing recent STM and transport experiments [Z. Ge, et al, arXiv:2510.12009] on 2D electron systems in the presence of random quenched impurities, we argue that the resulting low-density putative "solid" phase reported experimentally is better described as an Anderson solid with the carriers randomly spatially localized by impurities than as a Wigner solid where the carriers form a crystal due to an interaction-induced spontaneous breaking of the translational symmetry. In strongly disordered systems, the resulting solid is amorphous, which is adiabatically connected to the infinite disorder Anderson fixed point rather than the zero disorder Wigner crystal fixed point.

Figures (22)

• Figure 1: Estimation of disorder strength from experimental parameters and conductivity as a function of electron density. (a) Mobility as a function of the dimensionless parameter $\left(mV_0/\hbar^2\right)^2$ (a measure of the short-ranged disorder strength) given the reported values of $n_{\rm SR}$ and $n_{\rm LR}$ (blue curve). The red dotted line marks the value of the reported mobility -- 2000 $\text{cm}^2 \text{ V}^{-1} \text{ s}^{-1}$WangPrivateComm. The intersection is our estimate of $\left(mV_0/\hbar^2\right)^2$. (b) Conductivity for the low disorder density case using the values of $n_{\rm SR}$, $n_{\rm LR}$, and $\left(mV_0/\hbar^2\right)^2$. The blue dotted line denotes $r_S = 37$, and the green dotted line denotes the highest charge density at which localization is observed experimentally. (c) Same as (b) for the high disorder density case. The green dotted line denotes the highest charge density reported in the experiment. In both panels (b) and (c), the red dotted line denotes the IRM criterion, and the blue solid line corresponds to the conductivity. (d) Failure of the assumption $g_v = 1$: Mobility as a function of $\left(mV_0/\hbar^2\right)^2$ with $n = 2.5 \times 10^{12} \text{ cm}^{-2}$ (blue curve), does not intersect $\mu = 2000 \text{ cm}^2 \text{ V}^{-1} \text{ s}^{-1}$ for $\left(mV_0/\hbar^2\right)^2 > 0$.
• Figure 2: Transport phase diagrams as functions of experimental disorder parameters. (a)$\sigma/\left(e^2/\hbar\right)$ as a function of $r_s$ and $n_i/n$, where $\sigma$ is the conductivity, $n_i = n_{\rm SR} + n_{\rm LR}$, and we assume $n_{\rm SR} = n_{\rm LR}$. Experimentally reported $(r_s, n_i/n)$ pairs are shown as squares (electron solids) or circles (electron liquids) ge2025visualizingWangPrivateComm. (b)$\sigma/\left(e^2/\hbar\right)$ as a function of $n_i = n_{\rm SR} + n_{\rm LR}$ and $n$ on a logarithmic scale, again assuming $n_{\rm SR} = n_{\rm LR}$. Experimentally reported $(n_i, n)$ pairs are shown as squares (electron solids) or circles (electron liquids) ge2025visualizingWangPrivateComm. (c) Same as (a) for an earlier experiment xiang2025imaging on the same materials with holes as charge carriers, assuming a mobility of $240\,\mathrm{cm}^2\,\mathrm{V}^{-1}\,\mathrm{s}^{-1}$, where only $n_{\rm LR}$ contributes to $n_i$. (d) Same as (b) for the earlier experiment xiang2025imaging. In all figures, the green line denotes the IRM criterion, while the purple line corresponds to $r_S = 37$. For (b) and (d), the black line represents $n_i = n$.
• Figure 3: Long-range disorder phase diagram characterized by (a) many-body inverse participation ratio and (b) effective correlation length. $z$ represents disorder strength and $r_s$ is the Wigner-Seitz radius.
• Figure 4: Short-range disorder phase diagram characterized by (a) many-body inverse participation ratio and (b) effective correlation length. $z$ represents disorder strength and $r_s$ is the Wigner-Seitz radius.
• Figure S1: Left: mobility for $n_{\rm SR} = 3.5 \times 10^{11} \text{cm}^{-2}$ and $n_{\rm LR}$ is varied. Right: mobility for $n_{\rm SR} = 9.66 \times 10^{12} \text{cm}^{-2}$ and $n_{\rm LR}$ is varied.