Resistance Noise Scaling in a Dilute Two-Dimensional Hole System in GaAs

We have measured the resistance noise of a two-dimensional (2D) hole system in a high mobility GaAs quantum well, around the 2D metal-insulator transition (MIT) at zero magnetic field. The normalized noise power $S_R/R^2$ increases strongly when the hole density $p_s$ is decreased, increases slightly with temperature ($T$) at the largest densities, and decreases strongly with $T$ at low $p_s$. The noise scales with the resistance, $S_R/R^2\sim R^{2.4}$, as for a second order phase transition such as a percolation transition. The $p_s$ dependence of the conductivity is consistent with a critical behavior for such a transition, near a density $p^{*}$ which is lower than the observed MIT critical density $p_c$.

Figure 1

(a) $\rho$ vs $T$ for densities $p_s=(1.30$, 1.39, 1.43, 1.44, 1.48, 1.52, 1.57, 1.63, 1.74, 1.86, 1.96, 2.06, 2.16, $2.31)\times {10}^{10}{\mathrm{c}\mathrm{m}}^{-2}$ (from top to bottom). The dashed line is the $\rho (T)$ curve corresponding to the $p_s$ limit $p_c^{\prime }=1.44\times {10}^{10}{\mathrm{c}\mathrm{m}}^{-2}$, under which the activated law analysis is valid. (b) $S_V$ vs frequency at $p_s=1.75\times {10}^{10}{\mathrm{c}\mathrm{m}}^{-2}$ and $T=300\mathrm{m}\mathrm{K}$, for two currents $I=3$ and 1.5 nA. The continuous straight lines are fits of the law $A/f^{\alpha }$ with $\alpha =1.1$, and the dashed line is the fit for $I=3\mathrm{n}\mathrm{A}$ divided by 4. Inset: Schematic view of the Hall bar, showing the three voltages used in the correlation measurements.

Figure 2

(a) $S_R/R^2$ (1 Hz) vs density for six temperatures. (b) $S_R/R^2$ vs $T$, for eight densities indicated in units of ${10}^{10}{\mathrm{c}\mathrm{m}}^{-2}$. In (a) and (b), the lines are guides to the eye.

Figure 3

Normalized noise power at 1 Hz as a function of the resistance at various temperatures, and for all the densities investigated between $1.5\times {10}^{10}{\mathrm{c}\mathrm{m}}^{-2}$ and $1.78\times {10}^{10}{\mathrm{c}\mathrm{m}}^{-2}$. The line is a fit with the power law $S_R/R^2\sim R^{2.4}$.

Figure 4

(a) Conductivity vs density for three temperatures. The lines are fits with $\sigma \sim [p_s-p^{*}(T){]}^t$. (b) The same data as in (a), plotted as a function of $p_s^2$. The lines are fits with $\sigma \sim [p_s^2-p^{*}(T{)}^2{]}^t$. (c) Temperature dependence of $p^{*}$. The closed diamonds (open triangles) correspond to $\sigma \sim (p_s-p^{*}{)}^t$ [$\sigma \sim (p_s^2-p^{*2}{)}^t$]. Open circles: $p_s$ limit below which $\rho (T)$ can be fitted with an activation law $\propto \exp (T_0/T)$. At $T=0$, this corresponds to $p_s=p_c^{\prime }$. The shaded area is the domain where the activation law is valid.