Filling factor $\nu =1\mathrm{}$ bilayer electron systems in the quantum Hall regime have an excitonic-condensate superfluid ground state when the layer separation d is less than a critical value $d_c.$ On a quantum Hall plateau current injected and removed through one of the two layers drives a dissipationless edge current that carries parallel currents and a dissipationless bulk supercurrent that carries opposing currents in the two layers. In this paper we discuss the theory of finite supercurrent bilayer states, both in the presence and in the absence of symmetry breaking interlayer hybridization. Solutions to the microscopic mean-field equations exist at all condensate phase winding rates for zero and sufficiently weak hybridization strengths. We find, however, that collective instabilities occur when the supercurrent exceeds a critical value determined primarily by a competition between direct and exchange interlayer Coulomb interactions. The critical current is estimated using a local stability criterion and varies as ${(d}_c-{d)}^{1/2}$ when d approaches $d_c$ from below. For large interlayer hybridization, we find that the critical current is limited by a soliton instability of microscopic origin.

• Received 14 May 2003

DOI:https://doi.org/10.1103/PhysRevB.68.155318