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

TL;DR

This paper analyzes the crossover behavior of a quantum Hall interferometer at filling fraction 5/2, revealing how interference patterns depend on quasiparticle parity and bias voltage, using boundary conformal field theory methods.

Contribution

It provides an exact theoretical description of the odd-even crossover in a 5/2 quantum Hall interferometer via boundary conformal field theory techniques.

Findings

Interference pattern depends on quasiparticle parity and bias voltage.

Absorption of quasiparticles by the edge causes the crossover.

Exact expression for the crossover as a function of bias voltage.

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.