Robustness of quantum Hall interferometry

Abstract

Fabry-Pérot interferometry has emerged as a tool to probe anyon statistics in the quantum Hall effect. The interference phase is interpreted as a combination of a quantized statistical phase and an Aharonov-Bohm phase, proportional to the device area and the charge of the anyons propagating along the device edge. This interpretation faces two challenges. First, the edge states have a finite width and hence the device area is ill-defined. Second, multiple localized anyons may be present in states that overlap with the edge, and it may not be clear whether a second anyon traveling along the edge will go inside or outside the region with a localized anyon and therefore whether or not it should pick up a statistical phase. We show how one may overcome both challenges. In a case where only one chiral edge mode passes through the constrictions defining the interferometer, as when electrons in a constriction are in a Laughlin state with $\nu =1/(2n+1)$ or the integer state at $\nu =1$, we show that the interference phase can be directly related to the total electron charge contained in the interferometer. This holds for arbitrary electron-electron interactions and holds even if the bulk of the interferometer has a higher electron density than the region of the constrictions. In contrast to the device area or to the number of anyons inside a propagating edge channel, the total charge is well-defined. We examine, at the microscopic level, how the relation between charge and phase is maintained when there is a soft confining potential and disorder near the edge of the interferometer, and we discuss briefly the complications that can occur when multiple chiral modes can pass through the constriction.

arXiv comment13 pages, 3 figures

References in corpus (14)

• Direct observation of anyonic braiding statistics at the $\nu$=1/3 fractional quantum Hall state
• Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State
• Sharp and Smooth Boundaries of Quantum Hall Liquids
• Proposed experiments to probe the non-abelian ν=5/2 quantum Hall state
• Theory of the Fabry-Perot Quantum Hall Interferometer
• Magnetic field-tuned Aharonov-Bohm oscillations and evidence for non-Abelian anyons at v=5/2
• Influence of Interactions on Flux and Back-gate Period of Quantum Hall Interferometers
• Charge accumulation at the boundaries of a graphene strip induced by a gate voltage: Electrostatic approach
• Fractional charge and fractional statistics in the quantum Hall effects
• Imaging the Conductance of Integer and Fractional Quantum Hall Edge States
• Fractional Edge Reconstruction in Integer Quantum Hall Phases
• Flux superperiods and periodicity transitions in quantum Hall interferometers
• Thermal anyon interferometry in phonon-coupled Kitaev spin liquids
• Thermal interferometry of anyons in spin liquids

Cited by in corpus (14)

• Anyon braiding and telegraph noise in a graphene interferometer
• Half-integer conductance plateau at the $\nu =2/3$ fractional quantum Hall state in a quantum point contact
• Strongly coupled edge states in a graphene quantum Hall interferometer
• Aharonov-Bohm interference and the evolution of phase jumps in fractional quantum Hall Fabry-Perot interferometers based on bi-layer graphene
• Spin-statistics relation and the Abelian braiding phase for anyons in fractional quantum Hall effect
• Dissipation and dephasing in quantum Hall interferometers
• Anomalous Aharonov-Bohm Interference in the Presence of Edge Reconstruction
• Different fractional charges from auto- and cross-correlation noise in quantum Hall states without upstream modes
• Quantum Hall interferometry at finite bias with multiple edge channels
• Modified interferometer to measure anyonic braiding statistics
• Single electron interference and capacitive edge mode coupling generates ${\Phi }_0/2$ flux periodicity in Fabry-Perot interferometers
• Berry Phases in the Bosonization of Nonlinear Edge Modes
• Proposal for bulk measurement of braid statistics in fractional quantum Hall effect
• Quantum statistics and self-interference in extended colliders