Critical currents of ideal quantum Hall superfluids

Abstract

Filling factor ν = 1 bilayer electron systems in the quantum Hall regime have an excitoniccondensate superfluid ground state when the layer separation d is less than a critical value dc. 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 (dc − d) 1/2 when d approaches dc from below. For large inter-layer hybridization, we find that the critical current is limited by a soliton instability of microscopic origin.

Stability of Superflow for Ultracold Fermions in Optical Lattices

“…While our work is in part inspired by recent experiments demonstrating fermionic superfluidity in an optical lattice [11], a broader motivation is to explore how competing broken symmetry states, such as charge density waves, lead to a breakdown of superflow in uniform strongly correlated superfluids -this issue is of great importance for systems ranging from high temperature superconductors [12] to excitonic superfluids in quantum Hall bilayers [13].…”

Transport properties of quantum Hall bilayers. Phenomenological description

“…Theoretical prediction on superfluidity of bound electron-hole pairs in electron-hole bilayers [1][2][3][4] and, especially, in quantum Hall bilayers [5][6][7][8][9][10][11][12][13] has stimulated experimental study of the counterflow transport in such systems. In these experiments [14][15][16][17][18][19] electrical current is passed through one layer in a given direction and returned to the source through the other layer in the opposite direction.…”

Interlayer phase coherence and superfluidity of electron–hole pairs in multilayer quantum Hall systems

“…[12,13] that the excitonic phase coherent state in quantum Hall bilayers is unstable at interlayer distances d\1:2' B (' B is the magnetic length). The instability at large d is connected with a formation of a charge density wave state.…”

“…Extending the approach of Ref. [13] to the multilayer case we obtain the following expression for the energies of collective modes:…”