Critical Tunneling Currents in Quantum Hall Superfluids: Pseudospin-Transfer Torque Theory

At total filling factor $\nu=1$ quantum Hall bilayers can have an ordered ground state with spontaneous interlayer phase coherence. The ordered state is signaled experimentally by dramatically enhanced interlayer tunnel conductances at low bias voltages; at larger bias voltages inter-layer currents are similar to those of the disordered state. We associate this change in behavior with the existence of a critical current beyond which static inter-layer phase differences cannot be maintained, and examine the dependence of this critical current on sample geometry, phase stiffness, and the coherent tunneling energy density. Our analysis is based in part on analogies between coherent bilayer behavior and spin-transfer torque physics in metallic ferromagnets. Comparison with recent experiments suggests that disorder can dramatically suppress critical currents.