AC conductivity of a quantum Hall line junction

Abstract

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