Spin Polarization Dependence of the Coulomb Drag at Large $r_s$

We find that the temperature dependence of the drag resistivity between two dilute two-dimensional hole systems exhibits an unusual dependence upon spin polarization. Our main observation is that near the apparent metal-insulator transition, the temperature dependence of the drag, given by $T^{\alpha }$, weakens significantly with the application of a parallel magnetic field ($B_{||}$), with $\alpha$ saturating at half its zero field value for $B_{||}>B^{*}$, where $B^{*}$ is the polarization field.

Figure 1

${\rho }_D$ vs $T$ on a log-log scale at $p_m=2.15\times {10}^{10}{\mathrm{c}\mathrm{m}}^{-2}$, with $B_{||}\perp I$. Traces are for (from bottom) $B_{||}=0$, 2, 3, 4, 5.3, 8, 10, 12, and 14 T. Solid lines are the best linear fits of each trace. Inset (a): $\rho$ vs $B_{||}$ for different $T$. Inset (b): $\alpha$ vs $B_{||}$. $\alpha$ deduced from the slope of the linear fits in the main plot. $B_c=3\mathrm{T}$ and $B^{*}=5.3\mathrm{T}$ are indicated by the dashed lines.

Figure 2

${\rho }_D/T^2$ vs $T$ for (from bottom) $B_{||}=0$, 2, 3, 4, and 5.3 T. $p_m=2.15\times {10}^{10}{\mathrm{c}\mathrm{m}}^{-2}$, with $B_{||}\perp I$. Data at $B_{||}=B_c$ shown as open circles.

Figure 3

${\rho }_D$ vs $T$ on a log-log scale at $p_m=1.85\times {10}^{10}{\mathrm{c}\mathrm{m}}^{-2}$ with $B_{||}\parallel I$. Traces are for (from bottom) $B_{||}=0$, 1.2, 1.7, 2.5, 3.4, 5, 7.5, 10, and 12 T. Solid lines are the best linear fit of each trace. Inset (a): $\rho$ vs $B_{||}$. Inset (b): $\alpha$ vs $B_{||}$. $B_c=1.7\mathrm{T}$ and $B^{*}=3.4\mathrm{T}$ are indicated by the dashed lines.

Figure 4

$\alpha (B_{||})/\alpha (0)$ vs $B_{||}/B^{*}$ for $p_m=2.15$, 1.75, 1.5, and $1.25\times {10}^{10}{\mathrm{c}\mathrm{m}}^{-2}$, with $B_{||}\perp I$ and for $p_m=1.85\times {10}^{10}{\mathrm{c}\mathrm{m}}^{-2}$, with $B_{||}\parallel I$. Inset: $\alpha$ vs $p_m$ for $B_{||}=0$ and $B_{||}>B^{*}$.

Figure 5

${\rho }_D$ vs $T$ on a log-log scale, for $p_m=7.0\times {10}^{10}{\mathrm{c}\mathrm{m}}^{-2}$, with $B_{||}\parallel I$. Traces are for (from bottom) $B_{||}=0$, 10, and 16 T. Solid lines are the best linear fit of each trace. Inset (a): $\rho$ vs $B_{||}$, for $T=0.3$, 0.6, 0.9, and 1.2 K. Inset (b): $\alpha$ vs $B_{||}$, deduced from the linear fits in the main plot.