Vanishing Hall Conductance in the Phase Glass Bose Metal at Zero Temperature

Motivated in part by the numerical simulations which reveal that the energy to create a defect in a gauge or phase glass scales as L θ with θ < 0 for 2D, thereby implying a vanishing stiffness, we re-examine the relevance of these kinds of models to the Bose metal in light of the new experiments which reveal that the Hall conductance is zero in the metallic state that disrupts the transition from the superconductor to the insulator in 2D samples. Because of the particle-hole symmetry in the phase glass model, we find that bosonic excitations in a phase glass background generate no Hall conductance at the Gaussian level. Furthermore, this result persists to any order in perturbation theory in the interactions. We show that when particle-hole symmetry is broken, the Hall conductance turns on with the same power law as does the longitudinal conductance. This prediction can be verified experimentally by applying a ground plane to the 2D samples.