# Recent Developments in the Field of the Metal-Insulator Transition in Two Dimensions
## 6 Transport Evidence for a Sliding Quantum Electron Solid  
The insulating side of the metal-insulator transition has been extensively studied (see, e.g., [49; 50; 51; 52; 53]), but no definitive conclusion has been reached concerning the origin of the low-density state. The observed nonlinear current-voltage (\(I-V\)) curves were interpreted as either the manifestation of the depinning of an electron solid [54; 55; 50; 51; 52] or the breakdown of the insulating phase within traditional scenarios such as strong electric field Efros-Shklovskii variable range hopping [56] or percolation (see, e.g., Refs. [6; 57] and the references therein). The observation of broad-band voltage noise at the threshold \(I-V\) curves [50; 51; 52], as well as the attempts to probe the low-density state in perpendicular magnetic fields [58; 59; 60; 61; 53] also have not yielded information that allows a choice between the depinning of the electron solid or traditional mechanisms [6; 57]. Much confusion was introduced by the fact that many authors chose to interpret their data in terms of the Wigner crystal [62; 63; 64; 65; 66], ignoring mundane interpretations. Figure 5: Product of the Landé factor and effective mass as a function of electron density in a SiGe/Si/SiGe quantum well determined by measurements of the field of full spin polarization \(B^{*}\) (squares) and Shubnikov–de Haas oscillations (circles) at \(T\approx 30\) mK. The empty and filled symbols correspond to two samples. The experimental uncertainty corresponds to the data dispersion and is about 2% for the squares and about 4% for the circles (\(g_{0}=2\) and \(m_{0}=0.19\,m_{\rm e}\) are the values for non-interacting electrons; \(m_{\rm e}\) is the free electron mass; and \(g_{\rm F}\approx g_{0}\) is the \(g\)-factor at the Fermi level). The top inset shows schematically the single-particle spectrum of the electron system in a state preceding the band flattening at the Fermi level (solid black line). The dashed violet line corresponds to an ordinary parabolic spectrum. The occupied electron states at \(T=0\) are indicated by the shaded area. Bottom inset: the effective mass \(m_{\rm F}\) versus electron density determined by analysis of the temperature dependence of the amplitude of Shubnikov–de Haas oscillations, similar to [45]. The dashed line is a guide to the eye. From [43]. In [67], a significant breakthrough in the understanding of the origin of the low-density state has been reported. The authors observed two-threshold \(V-I\) characteristics with a dramatic increase in noise between the two threshold voltages at the breakdown of the insulating state. The noise in current, in the form of fluctuations with time, dramatically increases above the first threshold, \(V_{\text{th1}}\), and essentially disappears above the second threshold, \(V_{\text{th2}}\). The double threshold behavior is very similar to that known for the collective depinning of the vortex lattice in Type-II superconductors (see, e.g., [68]) (provided the voltage and current axes are interchanged). This strongly favors the sliding 2D quantum electron solid, whereas the double threshold behavior cannot be described within alternative scenarios (percolation or overheating). Rather than being an ideal Wigner crystal, however, the 2D electron system described here is likely to be closer to an amorphous solid, which is similar to the case of the vortex lattice in Type-II superconductors where the collective pinning was observed. In Figure 6, several low-temperature voltage-current curves at different electron densities in the insulating regime \(n_{\text{s}}<n_{\text{c}}\) are shown. The corresponding interaction parameter exceeds \(r_{\text{s}}\sim 20\).