Vanishing Hall Resistance at High Magnetic Field in a Double-Layer Two-Dimensional Electron System

At total Landau level filling factor ${\nu }_{\mathrm{t}\mathrm{o}\mathrm{t}}=1$ a double-layer two-dimensional electron system with small interlayer separation supports a collective state possessing spontaneous interlayer phase coherence. This state exhibits the quantized Hall effect when equal electrical currents flow in parallel through the two layers. In contrast, if the currents in the two layers are equal, but oppositely directed, both the longitudinal and Hall resistances of each layer vanish in the low-temperature limit. This finding supports the prediction that the ground state at ${\nu }_{\mathrm{t}\mathrm{o}\mathrm{t}}=1$ is an excitonic superfluid.

Figure 1

Schematic drawing of a mesa structure confining the 2DES. Arms 1, 2, 3, and 4 are for injecting and withdrawing current, while arms 5, 6, and 7 are for measuring voltages. The solid line indicates the current pathway through one 2DES layer; the dashed line indicates the pathway in the other layer. Gates are not shown.

Figure 2

Hall and longitudinal resistances (solid and dotted traces, respectively) in a low density double-layer 2DES at $T=50\mathrm{m}\mathrm{K}$. (a) Currents in parallel in the two layers. (b) Currents in counterflow configuration. Resistances determined from voltage measurements on one of the layers.

Figure 3

Development of a deep minimum in $R_{xy}^{\mathrm{C}\mathrm{F}}$ with decreasing effective layer separation (a) and falling temperature (b). In (a) data taken at various $d/\ell$ (1.48, 1.59, 1.66, 1.71, 1.75, and 2.29) are plotted versus inverse filling factor ${\nu }_{\mathrm{t}\mathrm{o}\mathrm{t}}^{-1}$. In (b) the fixed $d/\ell$ data, taken at $T=30$, 150, 200, 250, 300, and 500 mK, are plotted versus magnetic field.

Figure 4

Temperature dependences of various resistances and conductivities at ${\nu }_{\mathrm{t}\mathrm{o}\mathrm{t}}=1$ and $d/\ell =1.48$. (a) Parallel current flow. Open dots: $R_{xx}^{\parallel }$; closed squares: $R_{xy}^{\parallel }$. (b) Counterflow. Open dots $R_{xx}^{\mathrm{C}\mathrm{F}}$, closed squares $R_{xy}^{\mathrm{C}\mathrm{F}}$. (c) Parallel and counterflow longitudinal conductivities, ${\sigma }_{xx}^{\parallel }$ and ${\sigma }_{xx}^{\mathrm{C}\mathrm{F}}$, respectively.