Vortex state of a d-wave superconductor in high-T-c cuprates

We study theoretically the vortex state of a d-wave superconductor in a magnetic field parallel to the c axis. We find, except in the immediate vicinity of the superconducting transition temperature, that a square lattice tilted by pi/4 from the a axis gives the most stable configuration, which provides the simplest interpretation of a recent small angle neutron scattering experiment by Keimer et al. and a more recent scanning tunnel microscope experiment by Maggio-Aprile et al. The residual density of states is shown to follow a root B law in a wide field region consistent with an earlier prediction by Volovik. The effect of d-s mixture is also studied. The most important effect appears to be a suppression of the upper critical field at low temperatures by 5-10 %.