Effect of screening long-range Coulomb interactions on the metallic behavior in two-dimensional hole systems

We have developed a technique utilizing a double quantum well heterostructure that allows us to study the effect of a nearby ground plane on the metallic behavior in a GaAs two-dimensional hole system (2DHS) in a single sample and measurement cooldown, thereby maintaining a constant disorder potential. In contrast to recent measurements of the effect of ground-plane screening of the long-range Coulomb interaction in the insulating regime, we find surprisingly little effect on the metallic behavior when we change the distance between the 2DHS and the nearby ground plane.

Figure 1

(Color online) Schematic of the technique used to vary the distance $d$ to the ground plane, where the upper 2DHS is (a) occupied $(d=50\mathrm{nm})$ or (b) depleted $(d=340\mathrm{nm})$. (c) A comparison of the longitudinal (${\rho }_{xx}$, left axis) and Hall (${\rho }_{xy}$, right axis) resistances of the lower 2DHS at $p=6.6\times {10}^{10}{\mathrm{cm}}^{-2}$ with $V_{BG}=0\mathrm{V}$ for $d=340\mathrm{nm}$ (solid blue/dark gray lines) and $d=50\mathrm{nm}$ (dashed red/gray lines). The arrows indicate the relevant axes. The data for $d=50\mathrm{nm}$ have been duplicated and offset upward by $1\mathrm{k}\Omega ∕◻$ in ${\rho }_{xx}$ and $5\mathrm{k}\Omega$ in ${\rho }_{xy}$ (solid red/gray lines) for clarity, since the data for the two $d$ values overlap.

Figure 2

(Color online) A comparison of the temperature dependent longitudinal resistivity ${\rho }_{xx}\left(T\right)$ vs temperature $T$ for (a) a previously measured 2DHS in a similar single QW heterostructure (Ref. 8) and (b) the lower 2DHS of our device when the upper 2DHS is depleted $(d=340\mathrm{nm})$. The numbers beside each trace indicate the hole density in units of ${10}^{10}{\mathrm{cm}}^{-2}$.

Figure 3

(Color online) [(a)–(e)] The measured resistivity ${\rho }_{xx}\left(T\right)$ vs temperature $T$ for $d=50\mathrm{nm}$ (thin red/gray lines) and $d=340\mathrm{nm}$ (thick blue/dark gray lines) for five different densities $p$. The back gate bias was the same for the two $d$ values at each density. The dashed lines show the calculated phonon contributions (parameter free fits of Karpus’ theory) in each case. The percentage change in resistivity from $150\mathrm{mK}\text{to}0.7\mathrm{K}$ for $d=340\mathrm{nm}$ is shown for each panel.

Figure 4

(Color online) (a) $\Delta \sigma$ vs $T$ for $p=4.9\times {10}^{10}{\mathrm{cm}}^{-2}$ and $d=50\mathrm{nm}$. The data are the thin solid line and the linear fit is the thick dashed line. The error bars indicate the effect of varying the temperature range of the linear fits used to obtain $d({\sigma }_{\mathit{int}}∕{\sigma }_0)∕d(T∕T_F)$. Although the values slightly change, the observed trends are unaffected. (b) A plot of the metallicity $d({\sigma }_{\mathit{int}}∕{\sigma }_0)∕d(T∕T_F)$ vs $r_s$ for $d=340\mathrm{nm}$ (open squares) and $d=50\mathrm{nm}$ (open circles), and $r_s^{\mathit{\text{dipole}}}$ for $d=50\mathrm{nm}$ (closed circles). The dashed line is a guide to the eye for the trend exhibited by the $d=340\mathrm{nm}$ data vs $r_s^{\mathit{\text{bare}}}$ (open squares).