Maximal positive cross-correlation of current noise from Andreev reflection

For more than a decade it has been accepted that the phenomena of quantum transport in mesoscopic systems are intimately connected with the fermionic nature of carriers, both electrons and holes. The simplest fingerprint of statistical interaction is the sub-Poissonian shot noise measured in the quantum point contact. I The electronic Hanbury BrownTwiss2 experiment performed in the quantum Hall regime3,4 demonstrates strong anticorrelation of current fluctuations, the effect known as antibunching, characteristic for fermionic particles obeying the Pauli exclusion principle. Quantum transport in a hybrid normal-metal-superconductor (NS) junction involves yet another quasiparticle: the Cooper pair carrying an effective charge 2e. In the Andreev reflection regimeS e V ~ d (where V is the applied bias and d is the superconducting gap) the electron incident from the . normal part of the junction is reflected as a hole. The remaining charge 2e is absorbed into the superconductor region as a single Cooper pair. The effective charge of Cooper pairs leads to doubling of NS junction conductance l and also doubles the Fano factor of a tunneling barrier at the NS interface.6 It has been proposed few years ago? that the statistical properties of Cooper pairs can be investigated in the hybrid NS junction in a way analogous to the Hanbury BrownTwiss experiment. Fermionic antibunching still gives negative particle cross-correlations but the charge reversal in Andreev reflection may lead to positive charge or current correlations. The possibility to detect positive crosscorrelation in the NS junction?-12 is by no means a trivial prospect, as charge Andreev reflection is limited to energies within the superconducting gap. Still, the cartoon picture one keeps in mind is that of two Cooper-pair partners undergoing a separation into different leads and then subject to a correlation measurement. The cross-correlations are limited by Cauchy-Bunyakovsky-Schwarz (CBS) inequality which states that crosscorrelations never exceed autocorrelation. We shan can ideal splitting the situation when CBS inequality is saturated. Theoretical analysis of positive cross-correlations in NS junctions has addressed two simple geometries so far. In particular, in the presence of many modes in the leads chaotic mode mixing dominates so that random matrix theory (RMT) can PACS number(s): 73.50.Td, 73.40.Ns, 74.45.+c