Locking and unlocking of the counterflow transport in $\nu =1$ quantum Hall bilayers by tilting of magnetic field

The counterflow transport in quantum Hall bilayers provided by superfluid excitons is locked at small input currents due to a complete leakage caused by the interlayer tunneling. We show that the counterflow critical current $I_c^{\text{CF}}$ above which the system unlocks for the counterflow transport can be controlled by a tilt of magnetic field in the plane perpendicular to the current direction. The effect is asymmetric with respect to the tilting angle. The unlocking is accompanied by switching of the systems from the dc to the ac Josephson state. Similar switching takes place for the tunneling setup when the current flowing through the system exceeds the critical value $I_c^{\text{T}}$. At zero tilt the relation between the tunnel and counterflow critical currents is $I_c^{\text{T}}=2I_c^{\text{CF}}$. We compare the influence of the in-plane magnetic field component $B_{\parallel }$ on the critical currents $I_c^{\text{CF}}$ and $I_c^{\text{T}}$. The in-plane magnetic field reduces the tunnel critical current and this reduction is symmetric with respect to the tilting angle. It is shown that the difference between $I_c^{\text{CF}}$ and $I_c^{\text{T}}$ is essential at field $\left|B_{\parallel }\right|\lesssim {\varphi }_0/d{\lambda }_J$, where ${\varphi }_0$ is the flux quantum, $d$ is the interlayer distance, and ${\lambda }_J$ is the Josephson length. At larger $B_{\parallel }$ the critical currents $I_c^{\text{CF}}$ and $I_c^{\text{T}}$ almost coincide each other.

Figure 1

(Color online) Critical current densities (in $j_c$ units) vs the in-plane magnetic field (in $B_c^{\prime }$ units). The counterflow critical current $j_c^{\text{CF}}$ is shown by solid line and the tunnel critical current $j_c^{\text{T}}$ by dashed line.