Hole-Hole Interaction Effect in the Conductance of the Two-Dimensional Hole Gas in the Ballistic Regime

On a high-mobility two-dimensional hole gas (2DHG) in a $\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{l}\mathrm{A}\mathrm{s}$ heterostructure we study the interaction correction to the Drude conductivity in the ballistic regime, $k_{B}T\tau /\hslash >1$. It is shown that the “metallic” behavior of the resistivity ($d\rho /dT>0$) of the low-density 2DHG is caused by the hole-hole interaction effect in this regime. We find that the temperature dependence of the conductivity and the parallel-field magnetoresistance are in agreement with this description, and determine the Fermi-liquid interaction constant $F_0^{\sigma }$ which controls the sign of $d\rho /dT$.

Figure 1

(a) Diagram of electron scattering by an impurity and the Friedel oscillation it produced. (b) Temperature dependence of the resistivity at different hole densities near the crossover in the sign of $d\rho /dT$. (c),(d) Resistivity on the metallic side of the crossover (symbols), and contribution to $\rho (T)$ due to phonon scattering (solid lines).

Figure 2

(a) Impurity scattering contribution $\Delta \rho$ against dimensionless temperature at different $p$. [For clarity, curves in (a) and (b) are offset vertically from zero value at $T=0$.] (b) The same data as in (a) but in conductivity form, with linear fitting. (c) Fermi liquid parameter versus hole density. Open symbols show the result obtained from the analysis of $\rho (T)$ at zero magnetic field; closed symbols show the result from the analysis of the parallel-field magnetoresistance, shown in Fig. 4b.

Figure 3

(a) Dependence of the resistivity on parallel magnetic field at $T=50\mathrm{m}\mathrm{K}$ and $p=(1.43,1.57,1.75,2.03,2.26,2.49,2.83,3.36)\times {10}^{\mathrm{10}}{\mathrm{c}\mathrm{m}}^{-2}$, from top to bottom. (b) Scaled data, with an added curve $\rho (B_{||})$ for $p=8.34\times {10}^{10}{\mathrm{c}\mathrm{m}}^{-2}$; solid line is the result of the model [14]. Inset: dependence of the effective $g$ factor on the hole density, obtained from the value of $B_S$.

Figure 4

(a) Temperature dependence of the conductivity at $B_{\parallel }=B_S$ for different hole densities. Coefficient $\alpha =0.53$ is obtained for $p=(2.49,2.83)\times {10}^{10}{\mathrm{c}\mathrm{m}}^{-2}$; $\alpha =0.62$ for $p=2.26\times {10}^{10}{\mathrm{c}\mathrm{m}}^{-2}$; $\alpha =0.74$ for $p=2.03\times {10}^{10}{\mathrm{c}\mathrm{m}}^{-2}$; and $\alpha =0.92$ for $p=(1.43,1.57,1.75)\times {10}^{10}{\mathrm{c}\mathrm{m}}^{-2}$. Inset: $\rho (B_{\parallel })$ for $p=2.26\times {10}^{10}{\mathrm{c}\mathrm{m}}^{-2}$, at different temperatures: $T=0.1,0.2,0.3,0.45,0.6,0.8\mathrm{K}$. (b) Magnetoconductivity against $B_{\parallel }^2$, at $T=0.6\mathrm{K}$ for densities $p=(2.03,2.26,2.49,2.83,3.36)\times {10}^{10}{\mathrm{c}\mathrm{m}}^{-2}$.