Coupling of Josephson Currents in Quantum Hall Bilayers

We study ring-shaped (Corbino) devices made of bilayer two-dimensional electron gases in the total filling factor one quantized Hall phase, which is considered to be a coherent Bardeen-Cooper-Schrieffer-like state of interlayer excitons. Identical Josephson currents are observed at the two edges while only a negligible conductance between them is found. The maximum Josephson current observed at either edge can be controlled by passing a second interlayer Josephson current at the other edge. Because of the large electric resistance between the two edges, the interaction between them can only be mediated by the neutral interlayer excitonic ground state.

Figure 1

(a) Schematic of the Corbino device with a cross section. Variable current sources (arrows) are connected to the two edges at the top layers. Voltages are measured using separate contacts (not shown). In (b)–(e), current-voltage characteristics are shown, which are measured in the ${\nu }_T=1$ state at temperatures below 50 mK. The respective measurement configurations are shown in the insets. In configurations (b) and (c), the conductances at small voltages are small. With contacts at the same edges, (d) and (e), a Josephson-like $I\mathrm{\text{−}}V$ is measured indicating the exciton condensate. Note that the critical Josephson currents at the two edges are equal.

Figure 2

(a) Josephson effect measured at the outer edge with different constant currents passing through the inner edge contacts. The critical Josephson currents through the outer contacts are increased (decreased) if an additional current flows through the inner contacts in the opposite (same) direction. (b) Upper and lower (positive and negative) input critical currents (black dots) measured at the outer edge as function of the Josephson current passing through the inner ones. The white dots are the critical currents measured at the output of the lower layer. They deviate from the input ones at large currents because large interedge voltages cause a parasitic charge current.

Figure 3

(a) Outer-edge Josephson $I\mathrm{\text{−}}V$ characteristics with a larger range of compensating inner currents. The $I\mathrm{\text{−}}V$ characteristics are offset by ($I_{\mathrm{inner}}/2\mathrm{nA}$) mV, respectively. The numbers at the traces are the respective $I_{\mathrm{inner}}$ values (nA). The positive (upper) critical Josephson current can be more than doubled, while the negative (lower) one is reduced and even changes sign with sufficiently large compensation. (b) Plotting the voltages at the outer edge vs the one at the inner edge while the Josephson current is increased. The two voltages are effectively identical.