Fundamental properties of a vortex in a d-wave superconductor

The vortex core structure in a d-wave superconductor is analyzed on the basis of the quasi-classical Eilenberger theory beyond the Ginzburg-Landau framework. The current and magnetic field distributions around an isolated vortex break the circular symmetry observed in s-wave pairing and show fourfold symmetry, reflecting, the internal degrees of freedom in d-wave pairing, i.e., (k) over cap(x)(2) - (k) over cap(y)(2) in reciprocal space through the low lying quasi-particle excitations. The peculiar orientation of the flux line lattice observed recently in a cuprate is discussed in light of the present theory.