Crossed Andreev reflection in diffusive contacts

TL;DR

This paper investigates crossed Andreev reflection in diffusive multiterminal structures using the quasiclassical Keldysh-Usadel formalism, revealing how nonlocal currents depend on interface transparency and spacing, with implications for entanglement sources.

Contribution

It provides a theoretical analysis of nonlocal processes in diffusive normal metal-superconductor structures, highlighting the scaling and decay of crossed Andreev reflection and cotunneling effects.

Findings

Nonlocal currents depend on interface transparency squared.

Nonlocal conductances decay exponentially with interface spacing.

Both cotunneling and crossed Andreev reflection contribute equally to nonlocal current.

Abstract

Crossed Andreev reflection in multiterminal structures in the diffusive regime is addressed within the quasiclassical Keldysh-Usadel formalism. The elastic cotunneling and crossed Andreev reflection of quasiparticles give nonlocal currents and voltages (depending on the actual biasing of the devices) by virtue of the induced proximity effect in the normal metal electrodes. The magnitude of the nonlocal processes is found to scale with the square of the barrier transparency and to decay exponentially with interface spacing. Nonlocal cotunneling and crossed Andreev conductances are found to contribute equally to the nonlocal current, which is of relevance to the use of normal metal-superconducting heterostructures as sources of entanglement.