Nonuniversal behavior of scattering between fractional quantum Hall edges

Abstract

Among the predicted properties of fractional quantum Hall states are fractionally charged quasiparticles and conducting edge-states described as chiral Luttinger liquids. In a system with a narrow constriction, tunneling of quasi-particles between states at different edges can lead to resistance and to shot noise. The ratio of the shot noise to the backscattered current, in the weak scattering regime, measures the fractional charge of the quasi-particle, which has been confirmed in several experiments. However, the non-linearity of the resistance predicted by the chiral Luttinger liquid theory was apparently not observed in some of these cases. As a possible explanation for these discrepancies, we consider a model where a smooth edge profile leads to formation of additional edge states. Coupling between the current carrying edge mode and the additional phonon like mode can lead to {\it nonuniversal} exponents in the current-voltage characteristic, while preserving the ratio between shot noise and the back-scattered current, for weak backscattering. For special values of the coupling, one may obtain a linear I-V behavior.