Andreev-like Reflection in the Pfaffian Fractional Quantum Hall Effect

Abstract

We studied the tunnel transport between the edge of a Pfaffian fractional quantum Hall state and that of an integer quantum Hall state. Based on the duality argument between the strong and weak tunnelings, we found that an Andreev-like reflection appeared in the strong tunneling regime. We calculated the charge conductance in the weak and strong tunneling regimes for the low-voltage limit. In the weak tunneling limit, $dI}/dV$ was proportional to $V^{1/\hat{I}½}$ with bias voltage $V$ and $\hat{I}½=1/2$. By contrast, in the strong tunneling limit, $dI/dV$ was expressed by $(e^2/h)2\hat{I}½/(1+\hat{I}½)$ with a correction term. We expect that this condition can be realized experimentally at the point contact between a fractional quantum Hall state with $\hat{I}½=5/2$ and an integer quantum Hall state with $\hat{I}½=3$.