Interaction correction to the longitudinal conductivity and Hall resistivity in high-quality two-dimensional GaAs electron and hole systems

We study the corrections in the low temperature limit to both the longitudinal conductivity and Hall resistivity due to electron-electron interactions in high-quality GaAs systems. Using the recent theory of Zala et al. [Phys. Rev. B 64, 214204 (2001)] we find that the interaction corrections to the conductivity and Hall resistivity are consistent with each other in $n\text{−}\mathrm{Ga}\mathrm{As}$, although the agreement is not as good in $p\text{−}\mathrm{Ga}\mathrm{As}$. This suggests that interaction effects can explain the metallic drop in resistivity at $B=0$ in $n\text{−}\mathrm{Ga}\mathrm{As}$ systems, but more work is required to understand $p\text{−}\mathrm{Ga}\mathrm{As}$ systems.

Figure 1

(Color online) (a)–(c) Longitudinal conductivity ${\sigma }_{xx}$ vs $T$ from the $n\text{−}\mathrm{Ga}\mathrm{As}$ sample at the indicated carrier densities. Solid lines are fits of Eq. (1) to the data and arrows mark $T=0.15$ $T_F$.

Figure 2

Left panel (a)–(c) shows the Hall resistivity ${\rho }_{xy}$ at the indicated carrier densities (in $\times {10}^9{\mathrm{cm}}^{-2}$) for the $n\text{−}\mathrm{Ga}\mathrm{As}$ sample at temperatures ranging from $150\text{to}600\mathrm{mK}$. The inset shows the difference between the straight line fits at $T$ and $600\mathrm{mK}$, $\Delta {\rho }_{xy}={\rho }_{xy}\left(T\right)-{\rho }_{xy}\left(600\mathrm{mK}\right)$, the arrow indicates decreasing $T$. Values of the Hall slope are presented in the right panel (d)–(f) along with the fit. The shaded region indicates one standard deviation error in the fitting.

Figure 3

(Color online) (a) $B=0$ conductivity ${\sigma }_{xx}$ of the $p\text{−}\mathrm{Ga}\mathrm{As}$ sample after subtracting the weak localization correction $\Delta {\sigma }_{WL}$ at the indicated carrier densities (in $\times {10}^{10}{\mathrm{cm}}^{-2}$). (b) Hall resistivity ${\rho }_{xy}$ at $n_s=4.97\times {10}^{10}{\mathrm{cm}}^{-2}$ for $T$ from $150\text{to}900\mathrm{mK}$, and (c) the corresponding Hall slope and fit to Eq. (3). The shaded region indicates the error in the fitting.

Figure 4

Values of the Fermi liquid parameter $F_0^{\sigma }$ extracted from ${\sigma }_{xx}\left(T\right)$ at $B=0$ (solid) and ${\rho }_{xy}\left(T\right)$ (open) as a function of $n_s$ for the (a) $n\text{−}\mathrm{Ga}\mathrm{As}$ and (b) $p\text{−}\mathrm{Ga}\mathrm{As}$ samples.