Figure 1

(a) Schematic of a mesoscopic device geometry showing the 2DES (red) at the heterointerface and the dopant layer (light blue). (b) Linearity of $(d\mathit{ln}\sigma /{\mathit{dn}}_s){}^{-2/3}$ with $n_s$, where the traces have been shifted vertically for clarity (device C2367). (c) Conductivity $\sigma$ (device C2367) as a function of $n_s$ at different temperatures. The solid lines are the fits for the BKT transition [see Eq. $(1)$]. The bottom right inset shows data and BKT fits for conductivity $\sigma$ of device T546 vs $n_s$ at different magnetic fields and $T=262$ mK. The top left inset shows the model for percolation-based transport. The conductivity clearly shows a deviation from the power law exponent 4/3 that is expected for the case of classical percolation.Reuse & Permissions

Figure 2

(a) Differential resistivity measurements (A2678) as a function of dc source-drain bias $V_{\mathit{sd}}$ at $0.3$ K and two carrier densities (${10}^9$ cm${}^{-2}$) corresponding to zero-bias resistivities of $4$ $h/e^2$ and $16$ $h/e^2$. (b) Time traces of normalized conductivity fluctuations at three different source-drain biases at $n_s=4.54\times {10}^9$ cm${}^{-2}$. Data show significant broadband noise at bias of $V_0\approx 200$ $\mu$V. (c) The power spectral density of conductivity noise at the three biases, showing a typical $1/f^{\alpha }$ behavior, where $\alpha$ is the spectral exponent ($n_s=4.54\times {10}^9$ cm${}^{-2}$, $T=0.3$ K). (d) The plot of $\alpha$ as a function of dc bias which shows a peak magnitude of $\approx$2 around $V_0$. The solid line is a guide to the eye ($n_s=4.54\times {10}^9$ cm${}^{-2}$, $T=0.3$ K). (e) Normalized variance $\delta {\sigma }^2/{\sigma }^2$ as a function of dc bias across the sample at different carrier densities (in units of ${10}^9$ cm${}^{-2}$). The solid lines are a guide to the eye ($T=0.3$ K).Reuse & Permissions

Figure 3

(a–c) Temperature dependence of conductivity $\sigma$ in three devices of different setback distances at various densities (in units of ${10}^{10}$ cm${}^{-2}$). The solid lines are fits at the higher temperature range ($T>1.5$ K) for temperature-induced BKT transition [Eq. (1), $X=T$]. (d) Scaling of scattering function $f(T)$ (see text). A single parameter scaling can be observed (holding the parameter $\Theta$ for A2678 at $6.3\times {10}^9$ cm${}^{-2}$ as a reference). The line indicates an asymptotic behavior of $f(T)\approx 1/T^3$ for $T\ll \Theta$. The top right inset shows experimental $f(T)$ in various devices at different $n_s$ (${10}^{10}$ cm${}^{-2}$). The bottom left inset shows the scaling parameter $\Theta$ to increase with increasing disorder.Reuse & Permissions

Figure 4

(a) Evolution of $n_{\mathit{kT}}$ as a function of temperature at different magnetic fields $H_{\perp }$ in A2678. (b) Phase boundary of melting at $H_{\perp }=1T$, showing consistency in the fits for $n_{\mathit{kT}}$ and $T_{\mathit{kT}}$. Blue squares indicate $T_{\mathit{kT}}$ extracted at various densities, and red circles indicate $n_{\mathit{kT}}$ extracted at different temperatures. (c) Phase diagram of $n_{\mathit{kT}}$ in the $T$-$H_{\perp }$ space for A2678. The magnitude of $n_{\mathit{kT}}$ is indicated by the scale bar on the right. The quantum fluctuations, characterized by the normalized magnetic length $l_H/a_0^{\mathit{kT}}$ ($a_0^{\mathit{kT}}$ is $a_0$ evaluated at $n_s=n_{\mathit{kT}}$) and the classical melting parameter $\Gamma$ (see text) are evaluated at $n_{\mathit{kT}}$, and some of the traces are shown.Reuse & Permissions