Theory of fractional quantum Hall interferometers

Abstract

Interference of fractionally charged quasi-particles is expected to lead to Aharonov-Bohm oscillations with periods larger than the flux quantum. However, according to the Byers-Yang theorem, observables of an electronic system are invariant under an adiabatic insertion of a quantum of singular flux. We resolve this seeming paradox by considering a microscopic model of electronic interferometers made from a quantum Hall liquid at filling factor 1/m. An approximate ground state of such interferometers is described by a Laughlin type wave function, and low-energy excitations are incompressible deformations of this state. We construct a low-energy effective theory by restricting the microscopic Hamiltonian of electrons to the space of incompressible deformations and show that the theory of the quantum Hall edge so obtained is a generalization of a chiral conformal field theory. In our theory, a quasi-particle tunneling operator is found to be a single-valued function of tunneling point coordinates, and its phase depends on the topology determined by the positions of Ohmic contacts. We describe strong coupling of the edge states to Ohmic contacts and the resulting quasi-particle current through the interferometer with the help of a master equation. We find that the coherent contribution to the average quasi-particle current through Mach-Zehnder interferometers does not vanish after summation over quasi-particle degrees of freedom. However, it acquires oscillations with the electronic period, in agreement with the Byers-Yang theorem. Importantly, our theory does not rely on any ad-hoc constructions, such as Klein factors, etc. When the magnetic flux through an FP interferometer is varied with a modulation gate, current oscillations have the quasi-particle periodicity, thus allowing for spectroscopy of quantum Hall edge states.

The paper is entirely rewritten; 23 pages, 13 figures

References in corpus (20)

• Direct measurement of the coherence length of edge states in the Integer Quantum Hall Regime
• Realization of a Laughlin quasiparticle interferometer: Observation of fractional statistics
• Dephasing in the electronic Mach-Zehnder interferometer at filling factor 2
• Finite bias visibility of the electronic Mach-Zehnder interferometer
• Decoherence and single electron charging in an electronic Mach-Zehnder interferometer
• Primary-Filling e/3 Quasiparticle Interferometer
• Edge Channel Interference Controlled by Landau Level Filling
• Detecting non-Abelian Statistics with Electronic Mach-Zehnder Interferometer
• Decoherence and interactions in an electronic Mach-Zehnder interferometer
• Resonant dephasing in the electronic Mach-Zehnder interferometer
• Shot Noise in Anyonic Mach-Zehnder Interferometer
• Is the charge determined via shot noise measurements unique?
• Nonequilibrium Dephasing in an Electronic Mach-Zehnder Interferometer
• The Behavior of Electronic Interferometers in the Non-Linear Regime
• Quantum transport in electron Fabry-Perot interferometers
• The plasma picture of the fractional quantum Hall effect with internal SU(K) symmetries
• Multiparticle interference in electronic Mach-Zehnder interferometers
• Anomalous structure in the single particle spectrum of the fractional quantum Hall effect
• Mach-Zehnder interferometer in the Fractional Quantum Hall regime
• Transport in the Laughlin quasiparticle interferometer: Evidence for topological protection in an anyonic qubit

Cited by in corpus (16)

• Direct observation of anyonic braiding statistics at the $\nu$=1/3 fractional quantum Hall state
• Impact of bulk-edge coupling on observation of anyonic braiding statistics in quantum Hall interferometers
• Single quasiparticle and electron nano-emitter in the fractional quantum Hall regime
• Quantum Hall phases and plasma analogy in rotating trapped Bose gases
• Physical principles underlying the quantum Hall effect
• Hanbury Brown and Twiss Correlations in Quantum Hall Systems
• Unified time-dependent perturbative relations applied to spectroscopy through photo-drag current
• Incompressibility Estimates for the Laughlin Phase
• Chirality and Current-Current Correlation in Fractional Quantum Hall Systems
• Gauge Invariance and Anomalies in Condensed Matter Physics
• Finite width of anyons changes their braiding signature
• Zero Mode Tunnelling in a Fractional Quantum Hall Device
• Anyon braiding on the single edge of a fractional quantum Hall state
• Tunneling current and current correlations for anyonic quasiparticles of ν = 1/2 chiral Luttinger liquid in multi-edge geometries
• Probing anyon statistics on a single-edge loop in the fractional quantum Hall regime
• Single electron interference and capacitive edge mode coupling generates ${\Phi }_0/2$ flux periodicity in Fabry-Perot interferometers