Zeeman and orbital effects of an in-plane magnetic field in cuprate superconductors

We discuss the effects of a magnetic field applied parallel to the Cu-O (ab) plane of the high T_c cuprate superconductors. After briefly reviewing the Zeeman effect of the field, we study the orbital effects, using the Lawrence-Doniach model for layered superconductors as a guide to the physics. We argue that the orbital effect is qualitatively different for in-plane and interlayer mechanisms for superconductivity. In the case of in-plane mechanisms, interlayer couplings may be modeled as a weak interlayer Josephson coupling, whose effects disappear as H→∞; in this case Zeeman dominates the effect of the field. In contrast, in the interlayer mechanism the Josephson coupling is the driving force of superconductivity, and we argue that the in-plane field suppresses superconductivity and provides an upper bound for H_c2 which we estimate very crudely.