Even-odd effects in NSN scattering problems: Application to graphene nanoribbons

TL;DR

This paper investigates how lattice symmetry causes the crossed Andreev reflection probability to vanish in NSN junctions, especially in graphene nanoribbons, revealing an even-odd atomic number effect with implications for quantum transport.

Contribution

It demonstrates a novel even-odd atomic number effect in CAR probability in NSN junctions, specifically in graphene nanoribbons, under certain symmetry conditions.

Findings

CAR probability vanishes for even number of atoms in the superconducting region.

The effect applies to graphene nanoribbons with armchair and zigzag edges under specific conditions.

The robustness of the effect is analyzed against boundary smoothing and doping.

Abstract

We study crossed Andreev reflection (CAR) of electrons or holes in normal metal-superconductor-normal metal junctions and highlight some very strong effects of the underlying lattice. In particular, we demonstrate that for sharp interfaces and under certain, albeit generic, symmetry conditions, the CAR probability exactly vanishes for an even number of atoms in the superconducting region. This even-odd effect applies notably to NSN junctions made of graphene nano-ribbons with armchair edges and for zigzag edges with somewhat more restrictive conditions. We analyze its robustness towards smoothing of the boundaries or doping of the sample.