Counterflow Measurements in Strongly Correlated GaAs Hole Bilayers: Evidence for Electron-Hole Pairing

We study interacting GaAs bilayer hole systems, with very small interlayer tunneling, in a counterflow geometry where equal currents are passed in opposite directions in the two, independently contacted layers. At low temperatures, both the longitudinal and Hall counterflow resistances tend to vanish in the quantum Hall state at total bilayer filling $\nu =1$, demonstrating the pairing of oppositely charged carriers in opposite layers. The counterflow Hall resistance decreases much more strongly than the longitudinal resistances as the temperature is reduced.

Figure 1

(a) Schematic representation of the Hall bar mesa utilized in this study. Each lead contacts a particular layer (T: top; B: bottom) in the counterflow configuration. (b),(c) Illustration of the relations between the bilayer, counterflow, single-layer, and drag voltages and related transport coefficients. (d) ${\rho }_{xx}$ and ${\rho }_{xy}$ measured at $T=30\mathrm{m}\mathrm{K}$ in the bilayer configuration where all contacts are made to both layers. (e) ${\rho }_{xx}$ and ${\rho }_{xy}$ measured in the bottom layer in the counterflow configuration where equal and opposite currents are passed in the two layers. In (d) and (e) the layer densities are $p_{\mathrm{B}}=p_{\mathrm{T}}=2.75\times {10}^{10}{\mathrm{c}\mathrm{m}}^{-2}$.

Figure 2

$T$ dependence of various transport coefficients at $\nu =1$: counterflow, single-layer, and drag ${\rho }_{xx}$’s, and counterflow ${\rho }_{xy}$. Remarkably, the counterflow ${\rho }_{xy}$ remains much smaller than the counterflow ${\rho }_{xx}$ in the entire $T$ range. The two linear combinations of single-layer and drag transport coefficients, $({\rho }_{\mathrm{S}\mathrm{L}}-{\rho }_D)/2$ and ${\rho }_{\mathrm{S}\mathrm{L}}+{\rho }_D$, are also shown.

Figure 3

(a) Counterflow ${\rho }_{xx}$ and ${\rho }_{xy}$, bilayer ${\rho }_{xx}$, and (b) single (bottom) layer ${\rho }_{xy}$ and Hall drag vs $B$, all measured at $T=630\mathrm{m}\mathrm{K}$. As a consistency check, the sum of these two traces is shown in panel (a) as a dotted trace. The bilayer ${\rho }_{xx}$ is multiplied by 2 to normalize it to the layer current.

Figure 4

(a) Symmetric (${\sigma }_{+}$) and antisymmetric (${\sigma }_{-}$) conductivities vs $T^{-1}$ measured at $\nu =1$. (b) Counterflow ${\rho }_{xx}$ and ${\rho }_{xy}$ vs $T$.