Dissipation and Tunneling in Quantum Hall Bilayers

We discuss the interplay between transport and intrinsic dissipation in quantum Hall bilayers, within the framework of a simple thought experiment. We compute, for the first time, quantum corrections to the semiclassical dynamics of this system. This allows us to reinterpret tunneling measurements on these systems. We find a strong peak in the zero-temperature tunneling current that arises from the decay of Josephson-like oscillations into incoherent charge fluctuations. In the presence of an in-plane field, resonances in the tunneling current develop an asymmetric line shape.

Figure 1

Mean field (classical) spin trajectories are equipotentials on the surface of the spin sphere.

Figure 2

Decay processes for $V>V_0$. (a) Dominant process for $Q=0$: ${\epsilon }_{\mathit{q}}+{\epsilon }_{-\mathit{q}}=eV$. (b) Decay process at finite $Q$: ${\epsilon }_{\mathit{Q}}=eV$.

Figure 3

Plots of the current $I$ (arbitrary units) at $Q=0$ and at finite $Q=0.5(4\pi {\rho }_{E}S/v)$ so that $vQ\sim 150\mu \mathrm{V}$. The two spin wave contribution (2 sw) to the current gives rise to the asymmetric peak, as shown. The contributions at finite $Q$ have been broadened by a Gaussian distribution for $Q$ of width ${\sigma }_Q=0.1(4\pi {\rho }_{E}S/v)$.