The effects of interactions and disorder in the two-dimensional chiral metal

We study the two-dimensional chiral metal, which is formed at the surface of a layered three-dimensional system exhibiting the integer quantum Hall effect by hybridization of the edge states associated with each layer of the sample. We investigate mesoscopic fluctuations, dynamical screening and inelastic scattering in the chiral metal, focussing particularly on fluctuations of conductance, $\delta g(B)$, with magnetic field, $B$. The correlation function $<\delta g(B) \delta g(B+\delta B)>$ provides information on the inelastic scattering rate, $\tau_{in}^{-1}$, through both the variance of fluctuations and the range of correlations in $\delta B$. We calculate this correlation function for samples which are not fully phase coherent. Two regimes of behaviour exist, according to whether $\tau_{in}^{-1}$ is smaller or larger than $\tau_{\perp}^{-1}$, the rate for inter-edge tunneling, and we give results in both regimes. We also investigate dynamical screening of Coulomb interactions in the chiral metal and calculate the contribution to $\tau_{in}^{-1}$ from electron-electron scattering, finding $\tau_{in}^{-1} \propto T^{3/2}$ for $\tau_{in}^{-1} \ll \tau_{\perp}^{-1}$ at temperature $T$.