Non-equilibrium quantum noise in chiral Luttinger liquids

Abstract

We study non-equilibrium noise in Chiral Luttinger Liquids using the Landauer-Buttiker Scattering approach, obtaining the current/voltage noise spectrum for a four-terminal measurement scheme. Experimental consequences of the tunneling of charges are present in the four-terminal measurement of both the low-frequency shot noise ($ω$ near 0), and the high-frequency Josephson noise ($ω$ near $ω_J=e^*V/\hbar$). Within perturbation theory, an algebraic singularity is present (to all orders) at the Josephson frequency $ω_J=e^*V/\hbar$, whose position depends on the charge $e^*$ of the tunneling particles, either electrons or fractionally charged quasiparticles. We show in a non-perturbative calculation for an exactly solvable point that the singularity at the quasiparticle frequency exists only in the limit of vanishing coupling, whereas the singularity at the electron frequency is present for all coupling strengths. The vanishing coupling limit corresponds to perfectly quantized Hall conductance in the case of quasiparticle tunneling between edge states in the fractional quantum Hall regime, and thus tunneling destroys the singularity at the quasiparticle frequency concomitantly with the quantized current.