Vortex state in d-wave superconductivity

After a brief introduction on d-wave superconductivity, we review some unusual properties of vortex and vortex lattice in d-wave superconductivity. In a magnetic field B parallel c a square vortex lattice tilted by 45 from the a-axis is most stable except in the immediate vicinity of Tc the superconducting transition temperature or in a small magnetic field (say B≤1 T). Further in the vortex core, there are low-energy extended states (say vertical stroke E vertical stroke <0.2Δ) and a few bound states in contrast to the dense series of bound states in a vortex of conventional superconductors. In a magnetic field B in the a-b plane, both thermodynamic and transport properties exhibit fourfold symmetry, which should be readily accessible experimentally. (orig.)