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

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 $e\mathrm{/}m$ 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 $e\mathrm{/}m$ impinging on the second QPC can only be transmitted as charges $e$, with the reflection of holes of charge $e(1-m)\mathrm{/}m$. 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.