Anomalous Coulomb Drag in Electron-Hole Bilayers

We report Coulomb drag measurements on GaAs-AlGaAs electron-hole bilayers. The two layers are separated by a 10 or 25 nm barrier. Below $T\approx 1\mathrm{K}$ we find two features that a Fermi-liquid picture cannot explain. First, the drag on the hole layer shows an upturn, which may be followed by a downturn. Second, the effect is either absent or much weaker in the electron layer, even though the measurements are within the linear response regime. Correlated phases have been anticipated in these, but surprisingly, the experimental results appear to contradict Onsager’s reciprocity theorem.

Figure 1

(a) Generalized schematic of the devices. The $p$-doping and hole QW width vary between devices, as given in Table . (b) Photograph of the sample showing the alignment of the backgates. (c) Schematic of the circuit for Coulomb drag measurements. The backgate and the topgate are omitted for clarity.

Figure 2

(a) Data from device $A$. The drive current was 20 nA, 7 Hz for all the traces. The solid black lines are best fits to a $T^2$ behavior. The inset shows an expanded view of the lower trace at $n=p=1.0\times {10}^{11}{\mathrm{cm}}^{-2}$. The upturn was no longer observed at this density on the holes, but the downturn can be seen. (b) Raw data showing the linearity of drag voltage with drive current and (c) relatively flat behavior of the out-of-phase component ($V_y$) as measured by the lock-in, when the in-phase ($V_x$) component goes through an upturn and sign reversal.

Figure 3

Data from device $D$. The upturn and the beginning of the downturn are clearly seen. A much weaker effect is seen for the electrons than the holes. The inset shows that the measurements are clearly within the linear response regime.

Figure 4

(Left) Data from device $B$. The inset shows that the linearity of drag voltage and drive current is not compromised. (Right) Data from device $C$. In the main figure, the error bars represent the difference of the drag voltage measured by interchanging the drag and drive layers. The inset shows the expanded view of the upturn.

Figure 5

Data from device $D$, with a 10 nm ${\mathrm{Al}}_{0.9}{\mathrm{Ga}}_{0.1}\mathrm{As}$ barrier. The dotted vertical line in both panels denote the point where $n=p$. At this density, considering an effective peak-to-peak separation of $d=25\mathrm{nm}$, we get $d/l\approx 2$, with $l=1/\sqrt{(}2\pi n)$. The red triangles denote drag measured on the holes (${\rho }_{D,h}$), the blue squares denote drag measured on electrons (${\rho }_{D,e}$). The data at $T=1.55\mathrm{K}$ are repeated on both panels for comparison.