Spin superconductor in ferromagnetic graphene

Abstract

We show a spin superconductor in ferromagnetic graphene as the counterpart to the charge superconductor in which a spin-polarized electron-hole pair plays the role of the spin $2(\ensuremath{\hbar}/2)$ ``Cooper pair'' with a neutral charge. We present a BCS-type theory for the spin superconductor. With the ``London-type equations'' of the super-spin-current density, we show the existence of an electric ``Meissner effect'' against a spatial varying electric field. We further study a spin superconductor/normal conductor/spin superconductor junction and predict a spin-current Josephson effect.