ArXiv · 2026
We propose an average-current interferometer for the directional causal response of fractional quantum Hall edges. Three coherent quantum point contacts (QPCs) form a flux-enclosing loop, so the leading Aharonov-Bohm harmonic is cubic in tunneling. Interference between a direct transfer and a coherent two-step path resolves downstream and upstream propagation. For a local Laughlin edge at ν=1/m, the upstream coefficient vanishes exactly, while the downstream amplitude scales as E^(3ν-2). A weak finite-range nonlocal density interaction spanning the tunneling points activates the upstream coefficient without creating an upstream mode. At low temperature and unresolved delay, its amplitude scales as E^(2ν-1) and its aligned phase relative to the downstream reference is -π(1-ν)/2+χₐ modulo 2π, with χₐ=0 or π. Opposite cyclic voltage orderings isolate the two directions, while a folded same-filling Laughlin edge with a neutral weak link realizes a sign-tunable bridge. For a general Abelian edge, the device probes the directional content of the selected tunneling vertex. If δ_± are its downstream and upstream weights, its nonzero directional amplitudes scale as E^(3Δ_ℓ-2), with Δ_ℓ=δ₊+δ₋, and obey Aᵘ_ℓ/Aᵈ_ℓ=|sin(πδ₋)/sin(πδ₊)|. When both are nonzero, positive-flux alignment gives, after removal of a known fixed sign, the relative phase πΔ_ℓ=2π h_ℓ. In the same-vertex coherent unresolved-flight regime, the scaling dimension and directional ratio determine the exchange angle θ_ℓ=π(δ₊-δ₋) modulo 2π. The Aharonov-Bohm flux frequency additionally gives the charge, enabling separate extraction of quasiparticle charge, scaling dimension, and exchange angle.
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