Response of a superconductor to a Zeeman magnetic field

We study the response of a two-dimensional (Formula presented) superconductor to a magnetic field that couples only to the spins of the electrons. In contrast to the (Formula presented)-wave case, the (Formula presented) state is modified even at small magnetic fields, with the gap nodes widening into normal, spin polarized, pockets. We discuss the promising prospects for observing this in the cuprate superconductors in fields parallel to the Cu-O planes. We also discuss the phase diagram, inclusive of a finite momentum pairing state with a linkage between the momentum of the pairs and the nodes of the relative wave function.