Hall Conductivity near the z=2 Superconductor-Insulator Transition in 2D

Abstract

We analyze here the behavior of the Hall conductivity $σ_{xy}$ near a $z=2$ insulator-superconductor quantum critical point in a perpendicular magnetic field. We show that the form of the conductivity is sensitive to the presence of dissipation $η$, and depends non-monotonically on $H$ once $η$ is weak enough. $σ_{xy}$ passes through a maximum at $H \sim ηT$ in the quantum critical regime, suggesting that the limits $H \to 0$ and $η\to 0$ do not commute.