Long range Josephson coupling through ferromagnetic graphene

TL;DR

This paper investigates the Josephson effect in graphene-based superconductor-ferromagnet-superconductor junctions, revealing long-range coupling and temperature-induced phase transitions influenced by exchange fields and graphene properties.

Contribution

It introduces the concept of long-range Josephson coupling mediated by exchange interactions in ferromagnetic graphene, highlighting the role of Andreev-Klein processes and phase transitions.

Findings

Oscillatory Josephson coupling persists at high exchange fields.

Long-range coupling is enhanced in half-metallic graphene.

Temperature induces transitions between 0 and π phases.

Abstract

We study the Josephson effect in graphene-based ballistic superconductor-ferromagnet-superconductor (SFS) junctions. We find an oscillatory Josephson coupling $I_c R_N$ of F graphene whose amplitude is nonvanishing for a half-metallic graphene, increases for the exchange fields $h$ above the Fermi energy $E_{F}$ and shows only a slow damping at strong exchange fields $h\gg E_{F}$. We interpret this long range Josephson coupling as the result of the exchange mediated Andreev-Klein process at FS interfaces which enhances the induced antiparallel-spin superconducting correlations in F graphene by increasing $h$ above $E_{F}$. We further demonstrate the existence of regular temperature induced transitions between 0 and $\pi$ couplings in the plane of $T$ and $h$ where the phase boundaries have distinct shapes at the two regimes of $h$ below and above $E_{F}$.