Insulating behavior of dilute two-dimensional holes in GaAs under an in-plane magnetic field

Insulating resistivity of high mobility dilute two-dimensional holes in GaAs under an in-plane magnetic field exhibits a weak temperature dependence when the carrier density is higher than the critical density of zero-field metal-insulator transition. When the density is below the critical density, the temperature dependence is stronger and exhibits a crossover from the Mott variable range hopping to the Efros-Shklovskii variable range hopping as the field is increased.

Figure 1

$T$ dependence of $\rho$ at $B_{\Vert }=14\mathrm{T}$ for $p=4.33$, 2.26, 1.55, 0.94, and $0.79\times {10}^{10}{\mathrm{cm}}^{-2}$ from the bottom. Inset: $T$ dependence of $\rho$ at $B_{\Vert }=0\mathrm{T}$ for the same densities.

Figure 2

(a) $\rho$ in logarithmic scale plotted as a function of $1∕T^{1∕3}$ at $B_{\Vert }=14\mathrm{T}$ for $p=4.33$, 2.26, and $1.55\times {10}^{10}{\mathrm{cm}}^{-2}$ from the bottom. (b) $\rho$ vs $T$ at $B_{\Vert }=14\mathrm{T}$ in log-log scale for the same densities. The straight line for $p=1.55\times {10}^{10}{\mathrm{cm}}^{-2}$ is the best linear fit to the plot and indicates $\rho \approx 1∕T$.

Figure 3

(a) $\rho$ in logarithmic scale plotted as a function of $1∕T^{1∕2}$ at $B_{\Vert }=14$, 10, and 6 T (top axis) and as a function of $1∕T^{1∕3}$ at $B_{\Vert }=2$ and 1 T (bottom axis) for $p=0.79\times {10}^{10}{\mathrm{cm}}^{-2}$. (b) Exponent $x$, determined as a free parameter, vs $B_{\Vert }$.