Odd-Even Crossover in a non-Abelian $\nu =5/2$ Interferometer

Abstract

We compute the backscattered current in a double point-contact geometry of a Quantum Hall system at filling fraction $\nu =5/2$ as a function of bias voltage in the weak backscattering regime. We assume that the system is in the universality class of either the Pfaffian or anti-Pfaffian state. When the number of charge $e/4$ quasiparticles in the interferometer is odd, there is no interference pattern. However, the coupling between a charge $e/4$ quasiparticle and the edge causes it to be absorbed by the edge at low energies. Consequently, an interference pattern appears at low bias voltages and temperatures, as if there were an even number of quasiparticles in the interferometer. We relate this problem to that of a semi-infinite Ising model with a boundary magnetic field. Using the methods of perturbed boundary conformal field theory, we give an exact expression for this crossover of the interferometer as a function of bias voltage. Finally, we comment on the possible relevance of our results to recent interference experiments.

Two figures added, along with a brief explanation of them. Abstract slightly edited, and one reference added

References in corpus (12)

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Cited by in corpus (26)

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• Recent Experimental Progress of Fractional Quantum Hall Effect: 5/2 Filling State and Graphene
• Quasi-Topological Phases of Matter and Topological Protection
• Exact Solution for Bulk-Edge Coupling in the Non-Abelian $\nu =5/2$ Quantum Hall Interferometer
• Edge-mode velocities and thermal coherence of quantum Hall interferometers
• Telegraph noise and the Fabry-Perot quantum Hall interferometer
• Partial Equilibration of the Anti-Pfaffian edge due to Majorana Disorder
• Numerical Calculation of the Neutral Fermion Gap at $\nu =5/2$
• Non-Abelian Anyon Collider
• Thermopower of Quantum Hall States in Corbino Geometry as a Measure of Quasiparticle Entropy
• Braiding of Abelian and Non-Abelian Anyons in the Fractional Quantum Hall Effect
• Enhanced bulk-edge Coulomb coupling in Fractional Fabry-Perot interferometers
• Theory of non-Abelian Fabry-Perot interferometry in topological insulators
• Chiral correlators of the Ising conformal field theory
• Braiding of non-Abelian anyons using pairwise interactions
• Topological blockade and measurement of topological charge
• Size Constraints on Majorana Beamsplitter Interferometer: Majorana Coupling and Surface-Bulk Scattering
• Microwave Absorption by a Mesoscopic Quantum Hall Droplet
• Tunnelling current through fractional quantum Hall interferometers
• Alternation and interchange of e/4 and e/2 period interference oscillations as evidence for filling factor 5/2 non-Abelian quasiparticles
• Edge-Induced Qubit Polarization in Systems with Ising Anyons
• Local Magnetization in the Boundary Ising Chain at Finite Temperature
• Non-Fermi Liquid Quantum Impurity Physics from non-Abelian Quantum Hall States