Spin superconductor and electric dipole superconductor

We propose the concept of the spin superconductor (SSC), a counterpart to the charge superconductor. We carry out theoretical study to show the existence of a spin superconductor in a ferromagnetic graphene, in which the spin-polarized electron-hole excitons play the roles of the `Cooper' pairs. We present a BCS-type theory and the Laudau-Ginzburg theory for the SSC. 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 SSC/normal conductor/SSC junction and predict a spin-current Josephson effect. Recent experimental results showing spin superconductor in canted antiferromagnetic Cr2O3 via nonlocal spin transport will be reported.

By viewing the exciton in a bilayer system as an electric dipole, we provide a general theory for the electric dipole superconductivity, and derive the London-type and Ginzburg-Landau-type equations for the electric dipole superconductors. By using these equations, we discover the Meissner-type effect and the electric dipole current Josephson effect. These effects can provide direct evidence for the formation of the exciton superfluid state in bilayer systems and pave new ways to drive an electric dipole current.