Quasiparticle Andreev reflection in the Laughlin fractions of the fractional quantum Hall effect

TL;DR

This paper theoretically investigates quasiparticle Andreev reflection in the fractional quantum Hall effect using bosonization and Keldysh techniques, matching recent experimental results.

Contribution

It provides an analytical framework for understanding Andreev reflection in FQHE systems with two quantum point contacts, revealing temperature-dependent current correlations.

Findings

Current correlations reveal Andreev reflection signatures.

The ratio of auto- and cross-correlations indicates quasiparticle charge transfer.

Results align with recent experimental observations.

Abstract

Andreev reflection occurs in a normal metal-superconductor junction, when an electron on the normal side can only be transmitted as a Cooper pair in the superconductor, with the reflection of a hole on the normal side. A similar phenomenon can occur in strongly correlated systems, in particular in the fractional quantum Hall effect (FQHE), as the system quasiparticles have a charge $e/m$ different from the electron charge. We study theoretically a setup involving two quantum point contacts (QPC) in the FQHE where Andreev reflection occurs, as charges $e/m$ impinging on the second QPC can only be transmitted as charges $e$, with the reflection of holes of charge $e (1-m)/m $. Using the bosonization formalism, and out-of-equilibrium Keldysh Green function techniques, we provide a full analytical calculation of the current correlations at the outputs of the QPC, both at zero and finite temperature. The ratio between the auto- and cross-correlations of the output currents is a direct manifestation of Andreev reflection. Our results agree with recent experimental observations, and give precious information on the temperature dependence of this ratio.