Vanishing Hall conductance in the phase-glass Bose metal at zero temperature

Motivated in part by numerical simulations [H. G. Katzgraber and A. P. Young, Phys. Rev. B 66, 224507 (2002)PRBMDO0163-182910.1103/PhysRevB.66.224507; J. M. Kosterlitz and N. Akino, Phys. Rev. Lett. 81, 4672 (1998)PRLTAO0031-900710.1103/PhysRevLett.81.4672; Phys. Rev. Lett. 81, 4672 (1998)PRLTAO0031-900710.1103/PhysRevLett.81.4672] that reveal that the energy to create a defect in a gauge or phase glass scales as Lθ with θ<0 for two dimensions, thereby implying a vanishing stiffness, we reexamine the relevance of these kinds of models to the Bose metal in light of the new experiments [N. P. Breznay and Kapitulnik (unpublished); Y. Wang, I. Tamir, D. Shahar, and N. P. Armitage, arXiv:1708.01908 [cond-mat.supr-con]], which reveal that the Hall conductance is zero in the metallic state that disrupts the transition from the superconductor to the insulator in two-dimensional (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.