Local transport in a disorder-stabilized correlated insulating phase

We report the experimental realization of a correlated insulating phase in two-dimensional (2D) $\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}$ heterostructures at low electron densities in a limited window of background disorder. This has been achieved at mesoscopic length scales, where the insulating phase is characterized by a universal hopping transport mechanism. Transport in this regime is determined only by the average electron separation, independent of the topology of background disorder. We have discussed this observation in terms of a pinned electron solid ground state, stabilized by the mutual interplay of disorder and Coulomb interaction.

Figure 1

(Color online) (a) Conductivity $\left(\sigma \right)$ of mesoscopic samples as a function of electron density $n_s$ at $T\approx 0.3\mathrm{K}$. The crosses denote $n_s^{*}$ for individual samples (see text). Inset: $n_s$ dependence of $\sigma$ for a macroscopic Hall bar A77L. The solid line is the best fit of a classical percolationlike scaling relation $\sigma \sim {(n_s-n_c)}^{\gamma }$. (b) ${\delta }_{\mathrm{sp}}$ dependence of mobility at constant $n_s$ and $n_{\delta }$ for heterostructures similar to those used in presented work. (c) Resistivity $\left(\rho \right)$ as a function of temperature measured at $B_{\perp }=1\mathrm{T}$. The solid line represents a power law of $\sim T^{-1}$; the vertical lines in (c) and (d) indicate the Fermi temperatures $T_{\mathrm{F}}$. (d) Activation and saturation of $\rho$ at $B_{\perp }=1.5\mathrm{T}$.

Figure 2

Typical magnetoresistivity traces in four samples with varying levels of disorder. The vertical lines denote $\nu =1$. The numbers indicate electron density in units of ${10}^{10}{\mathrm{cm}}^{-2}$. $B_c$ denotes the field scale up to which a quadratic $B_{\perp }$ dependence could be observed. The parameters $\alpha$ and ${\rho }_{\mathrm{B}}$ were obtained from the slope and $y$ intercept of linear fits to $\ln \left(\rho \right)-B_{\perp }^2$ traces, respectively.

Figure 3

Absolute magnitude of $\alpha$ obtained from the slope of $\ln \left(\rho \right)-B_{\perp }^2$ traces for five different samples. The inset shows the same data in a log-log scale. The slope of the solid line is $-3∕2$.

Figure 4

(Color online) The dependence of ${\rho }_{\mathrm{B}}$ on the average electron separation $r_{\mathrm{ee}}$ in five different samples. The slope of the solid lines gives an estimate of $\xi$ [Eq. (1)].