Current Cross-Correlations in an Anyonic Mach-Zehnder Interferometer

Recent advancements in hybrid mesoscopic devices have opened up new avenues for studying edge excitations in quantum Hall (QH) systems. Typical experiments involve measuring the electrical and thermal conductances obtained from current-voltage characteristics at quantum point contacts (QPCs), which mix different edge channels. Many recent experiments have succeeded in constructing anyonic colliders at fractional filling factors (ν=1/3), with their results aligning with the predictions of Laughlin's theory at ν=1/3.

Motivated by this progress, in this work we use the nonequilibrium bosonization technique to study the collision of two dilute beams of quasiparticles in a Mach-Zehnder interferometer at filling factors ν=1/(2n+1). We calculate the tunnelling current, its zero frequency noise and the cross-correlation between the currents after scattering. The presence of two QPCs has some very interesting consequences; one of them being the modulation of ordinary Aharonov-Bohm oscillations by an asymmetry parameter ΔL, which is the length difference between the two junctions at the upper and lower chiral channels.

All calculations are also done for free fermions, i.e., at ν=1. We conclude the paper with the dependency of the ΔL modulated oscillations on the filling factor and discuss possible future extensions of the present work.