Critical Currents of Ideal Quantum Hall Superfluids

TL;DR

This paper develops a theoretical framework for understanding the critical supercurrents in ideal quantum Hall bilayer superfluids, analyzing stability and instabilities related to inter-layer interactions and hybridization.

Contribution

It introduces a comprehensive mean-field theory for finite supercurrents in quantum Hall bilayers, including effects of hybridization and predicts how critical currents depend on system parameters.

Findings

Critical current scales as (d_c - d)^{1/2} near the critical layer separation.

Collective instabilities limit supercurrent when exceeding a critical value.

Large hybridization induces a soliton instability that constrains supercurrent.

Abstract

Filling factor $\nu=1$ 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 inter-layer 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 inter-layer 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 inter-layer hybridization, we find that the critical current is limited by a soliton instability of microscopic origin.