Vortex state in NaxCoO2.yH2O: px+/-ipy-wave versus d(x2-y2)+/-id xy-wave pairing

Based on an effective Hamiltonian specified in the triangular lattice with possible p(x)+/-ip(y)- or dx(2)(-y(2))+/-id(xy)-wave pairing, which has close relevance to the newly discovered Na0.35CoO2.yH(2)O, the electronic structure of the vortex state is studied by solving the Bogoliubov-de Gennes equations. It is found that p(x)+/-ip(y) wave is favored for the electron doping as the hopping integral t<0. The lowest-lying vortex bound states are found to have, respectively, zero and positive energies for p(x)+/-ip(y)- and dx(2)(-y(2))+/-id(xy)-wave superconductors, whose vortex structures exhibit the intriguing sixfold symmetry. In the presence of strong on-site repulsion, the antiferromagnetic order and local ferromagnetic moment are induced around the vortex cores for the former and the latter, respectively, both of which cause the splitting of the local density of states peaks due to the lifting of spin degeneracy.