AC conductivity of a quantum Hall line junction

We present a microscopic model for calculating the AC conductivity of a finite length line junction made up of two counter- or co-propagating single mode quantum Hall edges with possibly different filling fractions. The effect of density-density interactions and a local tunneling conductance (σ) between the two edges is considered. Assuming that σ is independent of the frequency ω, we derive expressions for the AC conductivity as a function of ω, the length of the line junction and other parameters of the system. We reproduce the results of Sen and Agarwal (2008 Phys. Rev. B 78 085430) in the DC limit (ω→0), and generalize those results for an interacting system. As a function of ω, the AC conductivity shows significant oscillations if σ is small; the oscillations become less prominent as σ increases. A renormalization group analysis shows that the system may be in a metallic or an insulating phase depending on the strength of the interactions. We discuss the experimental implications of this for the behavior of the AC conductivity at low temperatures.