D-wave superconductors in a magnetic field

In the last three years we have witnessed remarkable successes of d-wave superconductivity in describing a variety of aspects of high-ir, superconducting cuprates. After a brief introduction about d-wave superconductors, we shall describe some of the properties of the vortex state in a magnetic field both B c and B a-b plane. In B c the square vortex lattice tilted by pi/4 from the a, axis appears to be the most stable except in the immediate vicinity of T = T-c, which has been seen recently by small angle neutron scattering and STM imaging experiments both on YBa2Cu3O6+x, monocrystals. Also both the residual density of states and the normal fluid density rho(N)(B) = 1 - rho(S)(B) depend on (B) over bar as first shown by Volovik. In B a-b the upper critical field exhibits a fourfold symmetry within the a-b plane.