Andreev-like Reflection in the Pfaffian Fractional Quantum Hall Effect

TL;DR

This paper investigates charge transport between Pfaffian fractional and integer quantum Hall edges, revealing an Andreev-like reflection in the strong tunneling regime and providing conductance formulas for different regimes.

Contribution

It introduces the concept of Andreev-like reflection in the Pfaffian fractional quantum Hall effect and derives conductance expressions for weak and strong tunneling regimes.

Findings

In the weak tunneling limit, conductance scales as V^{1/2}

In the strong tunneling limit, conductance approaches a constant with corrections

Andreev-like reflection appears in the strong tunneling regime

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 $V^{1/\nu}$ with bias voltage $V$ and $\nu=1/2$. By contrast, in the strong tunneling limit, $dI/dV$ was expressed by $(e^{2}/h)2\nu/(1+\nu)$ with a correction term. We expect that this condition can be realized experimentally at the point contact between a fractional quantum Hall state with $\nu=5/2$ and an integer quantum Hall state with $\nu=3$.