Vortex state in d-wave superconductivity

The vortex state in d-wave superconductivity exhibits a number of surprising features. In a magnetic field B parallel to c we find a square vortex lattice tilted by pi/4 from the a-axis is the most stable. Such a vortex lattice though elongated in the b-direction has been seen in a recent small angle neutron scattering experiment and STM imaging both on YBCO monocrystals. When B is in the a-b plane the upper critical field exhibits the fourfold symmetry in theta, where theta is the angle B makes from the a-axis. Again this fourfold symmetry is seen recently by a sensitive torque measurement in an untwinned YBCO monocrystal.