Magnet Field Induced idxy Order in a dx2-y2 Superconductor

The interaction between planar quasiparticles in a dx2-y2 superconductor and quantized vortices associated with a magnetic field perpendicular to the plane is shown to induce a pair potential with dxy symmetry, out a phase with dx2-y2 order. A microscopic calculation of a process involving quasiparticle scattering by the supercurrent around a vortex and Andreev reflection from its core is presented. Other processes also leading to an idxy pair potential are discussed. It is argued that such a fully gapped state may be the high field low temperature phase observed by Krishana, Ong et al in magnetothermal conductivity measurements of superconducting single crystal {\em Bi} - 2212.