Edge Dynamics in Quantum Hall Bilayers II: Exact Results with Disorder and Parallel Fields

Abstract

We study edge dynamics in the presence of interlayer tunneling, parallel magnetic field, and various types of disorder for two infinite sequences of quantum Hall states in symmetric bilayers. These sequences begin with the 110 and 331 Halperin states and include their fractional descendants at lower filling factors; the former is easily realized experimentally while the latter is a candidate for the experimentally observed quantum Hall state at a total filling factor of 1/2 in bilayers. We discuss the experimentally interesting observables that involve just one chiral edge of the sample and the correlation functions needed for computing them. We present several methods for obtaining exact results in the presence of interactions and disorder which rely on the chiral character of the system. Of particular interest are our results on the 331 state which suggest that a time-resolved measurement at the edge can be used to discriminate between the 331 and Pfaffian scenarios for the observed quantum Hall state at filling factor 1/2 in realistic double-layer systems.