Tunneling current and current correlations for anyonic quasiparticles of a ν=12 chiral Luttinger liquid in multiedge geometries

We consider anyonic quasiparticles with charge $e/2$ described by the $\ensuremath{\nu}=1/2$ chiral Luttinger liquid, which collide in a Hong--Ou--Mandel-like interferometer. These colliding anyonic channels can be formally viewed as hosting Laughlin-like fractional $\ensuremath{\nu}=1/2$ quasiparticles. More specifically, two possible geometries are considered: (i) a two-edge-channel setup where anyons originate from equilibrium reservoirs; and (ii) a four-edge-channel setup where nonequilibrium anyons arrive at the collider in the form of diluted beams. For both setups, we calculate the tunneling current and the current correlations. For setup (i), our results provide analytically exact expressions for the tunneling current, tunneling-current noise, and cross-correlation noise. An exact relation between conductance and noises is explicitly demonstrated. For setup (ii), we show that the tunneling current and the generalized Fano factor [defined in B. Rosenow et al. (2016)] are finite for diluted streams of $\ensuremath{\nu}=1/2$ anyons. This is due to the processes where nonequilibrium anyons, supplied via either source edge, directly tunnel at the central QPC. Thus, to obtain meaningful results in this case, one should go beyond the so-called time-domain braiding processes, where nonequilibrium anyons do not tunnel at the collider, but rather indirectly influence the tunneling by braiding with the quasiparticle-quasihole pairs created at the collider. This suggests that the effect of direct tunneling and collisions of diluted anyons in the Hong-Ou-Mandel interferometer can be important for various observables in physical quantum-Hall edges at Laughlin filling fractions.