Theory of large tunneling magnetoresistance in a gapped graphene-based ferromagnetic superconductor F/(FS) junction

Coexistence of superconductivity and ferromagnetism in a gapped graphene-based system (FS) is theoretically investigated. The center-of-mass momentum, P  , of a Cooper pair in FS is found to be P∼2Eex/ℏvF1-(m/EFS)2, where m, Eex, EFS are the rest mass energy of the Dirac electron, exchange energy and the Fermi energy in the superconductor FS, respectively. It is unlike the nature in a conventional FFLO state where P∼2Eex/ℏvFP∼2Eex/ℏvF. This work studies the magneto effect on the transport property of a F/(FS) junction where F is a ferromagnetic gapless graphene. In this work, FS is achieved by depositing a conventional ferromagnetic s-wave superconductor on the top of gapped graphene sheet. The Zeeman splitting in FS induces spin-dependent Andreev resonance. The conductances effected by both spin-dependent specular Andreev reflections and spin-dependent Andreev resonances are investigated. The interplay between the spin-dependent specular Andreev reflection in the F region and the spin-dependent Andreev resonance in the FS region causes a very large tunneling magnetoresistance |TMR| ∼ 3000% for m → EFS, possibly valuable in the graphene-based spintronic devices. This is because of the coexistence of the superconductivity and ferromagnetism in FS and the relativistic nature of electrons in graphene.