Thermodynamic Density of States of Two-Dimensional GaAs Systems near the Apparent Metal-Insulator Transition

We perform combined resistivity and compressibility studies of two-dimensional hole and electron systems which show the apparent metal-insulator transition—a crossover in the sign of $\partial R/\partial T$ with changing density. No thermodynamic anomalies have been detected in the crossover region. Instead, despite a tenfold difference in $r_s$, the compressibility of both electrons and holes is well described by the theory of nonlinear screening of the random potential. We show that the resistivity exhibits a scaling behavior near the percolation threshold found from analysis of the compressibility. Notably, the percolation transition occurs at a much lower density than the crossover.

Figure 1

Capacitance of a double-layer 2DEG structure E01 measured simultaneously by two methods: $C_b$—field penetration, $C$—capacitance; $T=4.2\mathrm{K}$, $f=4\mathrm{Hz}$. Inset: diagrams of capacitance measurements in (a) double- and (b) single-layer structures.

Figure 2

$d^{*}$ for 2DEG structure E01 with $s=200\AA$, $s_1=700\AA$, $s_2=400\AA$. Solid lines are the results of the field-penetration method, dashed line—the capacitance method. Dotted line—the NST theory with $n_i=1.2\times {10}^{11}{\mathrm{cm}}^{-2}$. [The donor concentration found from ${\tau }_q(n)$ is $n_i^{\tau }=2.3-4.5\times {10}^{11}{\mathrm{cm}}^{-2}$, while the maximum concentration of (uncorrelated) donors is $n_i^G=9.0\times {10}^{11}{\mathrm{cm}}^{-2}$.] Inset: comparison with 2DEG structure E02 ($s=400\AA$, $s_1=900\AA$, $s_2=500\AA$), where $n_i=2.2\times {10}^{11}{\mathrm{cm}}^{-2}$ and $n_i^{\tau }=3-4.5\times {10}^{11}{\mathrm{cm}}^{-2}$, while $n_i^G=11\times {10}^{11}{\mathrm{cm}}^{-2}$).

Figure 3

$d^{*}$ for 2DHG structures H03 and H05 with $s=500\AA$ and $s_1=2670\AA$, obtained by the capacitance method. Dotted lines—NST theory. The dopant concentrations for H03 are: $n_i=1\times {10}^{11}{\mathrm{cm}}^{-2}$, $n_i^{\tau }=1.1-2.2\times {10}^{11}{\mathrm{cm}}^{-2}$ and $n_i^G=5.6\times {10}^{11}{\mathrm{cm}}^{-2}$. The minimum for H05 ($n_i=2.4\times {10}^{11}{\mathrm{cm}}^{-2}$, $n_i^G=5.6\times {10}^{11}{\mathrm{cm}}^{-2}$) is shifted to larger $n$. Inset: $d^{*}$ for H03 (cooldown 2), $n_i=1.5\times {10}^{11}{\mathrm{cm}}^{-2}$ and $n_i^G=5.6\times {10}^{11}{\mathrm{cm}}^{-2}$.

Figure 4

(a) Fits of the conductance to $\sigma (n)=\alpha (n-n_p^{\sigma }{)}^t$. (b) An example of the temperature dependence of the resistivity of H03 structure. The range of $n_c$ in this cooldown is indicated by the dotted line.