Hanbury Brown-Twiss interferometry at the $\nu=2/5$ fractional quantum Hall edge

We propose a Hanbury Brown-Twiss interferometer for a $\nu=2/5$ fractional quantum Hall edge system, in which quasiparticles tunnel between two co-propagating edge modes. In contrast to the previously studied anyonic Fabry-P\'{e}rot and Mach-Zehnder interferometers, the proposed setup relies purely on two-particle interference rather than single-particle interference. In the weak-tunneling regime, we employ a bosonized edge theory together with Keldysh perturbation theory to evaluate the cross-correlation of the tunneling currents. In the large-device limit, we obtain an analytic expression for the flux-dependent noise, whose structure closely resembles that of an electronic HBT interferometer, but with the electron charge replaced by the fractional charge $e^{\star}=e/3$ and with scaling dimensions characteristic of the fractional edge modes. In this limit, the explicit anyonic exchange phases cancel, whereas when the device size becomes comparable to the thermal length, the cross-correlation may recover a more explicit dependence on the anyonic statistical angle.