Andreev bound states in ferromagnet-superconductor nanostructures

We discuss the properties of a ferromagnet - superconductor heterostructure on the basis of a Hubbard model featuring exchange splitting in the ferromagnet and electron - electron attraction in the superconductor. We have solved the spin - polarized Hartree - Fock - Gorkov equations together with the Maxwell's equation (Ampere's law) fully self-consistently. We have found that a Proximity Effect - Fulde - Ferrell - Larkin - Ovchinnikov state is realized in such a heterostructure. It manifests itself in an oscillatory behavior of the pairing amplitude in the ferromagnet and spontaneously generated spin polarized current in the ground state. We argue that it is built up from the Andreev bound states, whose energy can be tuned by the exchange splitting and hence can coincide with the Fermi energy giving rise to a current carrying $\pi$-state. We also suggest experiments to verify these predictions.