Spectroscopy of Quantum Hall Edge States at Complex Filling Factors

Abstract

We propose direct experimental tests of the effective models of fractional quantum Hall edge states. We first illustrate the effective models classification with the example of a quantum Hall fluid at filling factor 2/3. We show that, in this example, it is impossible to describe the edge states with only one chiral channel and that there are several inequivalent models of the edge states with two fields. We focus our attention on the four simplest models of the edge states of a fluid with filling factor 2/3 and evaluate charges and scaling dimensions of quasi-particles. We study transport through an electronic Fabry-Perot interferometer and show that scaling properties of the Fourier components of Aharonov-Bohm oscillations in the current provide information about the electric charges and scaling dimensions of quasi-particles. Thus, such interferometers can be used to discriminate between different effective models of fluids corresponding to the same filling factor.