Mach-Zehnder interferometry of fractional quantum Hall edge states

Abstract

We propose direct experimental tests of the effective models of fractional quantum Hall edge states. We first recall a classification of effective models based on the requirement of anomaly cancellation and illustrate the general 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 Mach-Zehnder 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 Mach-Zehnder interferometers can be used to discriminate between different effective models of fluids corresponding to the same filling factor. They therefore can be used to test fundamental postulates underlying the low-energy effective theory of edge states. An important ingredient of our analysis is the tunneling Hamiltonian of quasi-particles, the form of which is discussed in detail.

22 pages, 11 figures; published version

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Cited by in corpus (23)

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• Physical principles underlying the quantum Hall effect
• Theory of fractional quantum Hall interferometers
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• Scattering theory approach to bosonization of non-equilibrium mesoscopic systems
• Fluctuation dissipation relations for strongly correlated out-of-equilibrium circuits
• Transmission of heat modes across a potential barrier
• Interaction effects in a multi-channel Fabry-Pérot interferometer in the Aharonov-Bohm regime
• Chirality and Current-Current Correlation in Fractional Quantum Hall Systems
• Effective field theories for the $\nu =5/2$ edge
• Exact Dirac-Bogoliubov-de Gennes Dynamics for Inhomogeneous Quantum Liquids
• Universal non-equilibrium states at the fractional quantum Hall edge
• Tunnelling current through fractional quantum Hall interferometers
• Temperature dependence of the visibility in an electronic Mach-Zehnder interferometer
• Effective field theory and tunneling currents in the fractional quantum Hall effect
• Finite frequency noise for edge states at filling factor $\nu =2/5$
• FQHE interferometers in strong tunneling regime. The role of compactness of edge fields
• Tunneling current and current correlations for anyonic quasiparticles of ν = 1/2 chiral Luttinger liquid in multi-edge geometries
• Extracting the scaling dimension of quantum Hall quasiparticles from current correlations