Abstract
In the last three years we have witnessed remarkable successes ofd-wave superconductivity in describing a variety of aspects of high-T c superconducting cuprates. After a brief introduction aboutd-wave superconductors, we shall describe some of the properties of the vortex state in a magnetic field both Bc and Ba−b plane. In Bc the square vortex lattice tilted by π/4 from thea axis appears to be the most stable except in the immediate vicinity ofT=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 densityρ N(B)=1−ρ s(B) depend on\(\bar B\) as first shown by Volovik. In Ba−b the upper critical field exhibits a fourfold symmetry within thea−b plane.
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