Testing edge chirality with a three-path fractional quantum Hall interferometer

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 $\nu=1/m$, the upstream coefficient vanishes exactly, while the downstream amplitude scales as $E^{3\nu-2}$. 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 $E^{2\nu-1}$ and its aligned phase relative to the downstream reference is $-\pi(1-\nu)/2+\chi_a$ modulo $2\pi$, with $\chi_a=0$ or $\pi$. 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 $\delta_\pm$ are its downstream and upstream weights, its nonzero directional amplitudes scale as $E^{3\Delta_\ell-2}$, with $\Delta_\ell=\delta_++\delta_-$, and obey $A^u_\ell/A^d_\ell=|\sin(\pi\delta_-)/\sin(\pi\delta_+)|$. When both are nonzero, positive-flux alignment gives, after removal of a known fixed sign, the relative phase $\pi\Delta_\ell=2\pi h_\ell$. In the same-vertex coherent unresolved-flight regime, the scaling dimension and directional ratio determine the exchange angle $\theta_\ell=\pi(\delta_+-\delta_-)$ modulo $2\pi$. The Aharonov-Bohm flux frequency additionally gives the charge, enabling separate extraction of quasiparticle charge, scaling dimension, and exchange angle.