Gauge Fields and Composite Fermions in Bilayer Quantum Hall Systems

When placed in a strong magnetic field, a two-dimensional electron gas can exhibit the quantum Hall effect in which a step like pattern forms in the Hall resistance, RH , which is defined to be the voltage drop perpendicular to the current driven through the plane of the sample divided by the magnitude of the current. The filling fraction ν = p/q defines the quantization condition where p and q are relatively prime integers and q is odd, with RH =h/(ν e2) where h is Planck's constant and e is the charge of the electron. At the same time the Hall resistance becomes quantized the longitudinal resistance vanishes indicating dissipationless current flow. The integer quantum Hall effect (ν = 1, 2, 3...) is simply modeled using single-particle energy levels while the many-body fractional quantum Hall effect can be understood in terms of new particles known as composite fermions, electrons bound to an even number of statistical flux quanta. In this approach, the fractional quantum Hall effect for electrons is viewed as an effective integer quantum Hall effect for composite fermions. It was pointed out by Halperin, Lee and Read that for filling fraction ν = 1/2 the external magnetic field is exactly canceled by the average of the statistical flux quanta attached to the composite fermions. As a result, the composite fermions move in zero effective magnetic field with a well-defined Fermi surface at zero temperature. This "metallic" state is compressible and does not have a quantized Hall resistance. However, when two ν = 1/2 layers are brought close together, interactions between the layers lead to a new incompressible bilayer quantum Hall state in which electrons form a exciton condensate with total filling fraction νT = 1/2 + 1/2 = 1. Recently it has been proposed that an interesting new transition may occur in this system in which interlayer Coulomb repulsion leads to excitonic condensation not of electrons but of composite fermions which are then free to tunnel coherently between layers, despite the fact that there is no physical tunneling of electrons between layers. We find that this coherent tunneling is strongly suppressed by the layer-dependent Aharonov-Bohm phases experienced by composite fermions as they propagate through the fluctuating gauge fields associated with the statistical flux attached to the composite fermions. This suppression is analyzed by treating these gauge fluctuations within the random-phase approximation and calculating their contribution to the energy cost for forming an exciton condensate of composite fermions. Physically, this suppression manifests itself through the appearance of a positive, singular contribution to the ground state energy which grows with increasing φ, where φ is the order parameter characterizing the interlayer coherent state. This energy cost leads to (1) an increase in the critical interlayer repulsion needed to drive the transition; and (2) a discontinuous jump in the energy gaps to out-of-phase excitations (i.e., excitations involving currents with opposite signs in the two layers) at the transition.