AC conductivity of a quantum Hall line junction

TL;DR

This paper develops a microscopic model to calculate the AC conductivity of quantum Hall line junctions, accounting for interactions and tunneling, revealing oscillatory behavior and phase transitions influenced by system parameters.

Contribution

It provides exact expressions for AC conductivity in quantum Hall line junctions with interactions and tunneling, extending previous DC results and analyzing phase behavior.

Findings

AC conductivity exhibits oscillations depending on frequency and tunneling conductance.

System can be metallic or insulating based on interaction strength.

Results have implications for low-temperature experiments on quantum Hall systems.

Abstract

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 the tunneling conductance (\sigma), between the two edges, is considered, and exact expressions are derived for the AC conductivity as a function of the frequency (\omega), the length of the line junction and other parameters of the system. We reproduce the results of Phys. Rev. B 78, 085430 (2008) in the DC limit (\omega \to 0), and generalize those results for an interacting system. As a function of \omega, the AC conductivity shows significant oscillations if \sigma is small; the oscillations become less prominent as \sigma 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.