Probing the d-wave pairing symmetry in cobaltate superconductors by a local impurity

To provide clues for experimental clarification of the pairing mechanism in cobaltate superconductors, we investigate two possible pairing symmetries, chiral $d+id$ and d_xy waves, by making use of impurity effects. We consider both nearest-neighbor and next-nearest-neighbor pairing cases in real space. As expected, the superconducting order parameter exhibits a four-fold symmetric pattern in the nodal d_xy-wave state while displaying a six-fold symmetry in the case of chiral $d+id$ pairing. By calculating the local density of states for various doping levels, we show the existence of quasiparticle bound states inside the gap in all cases. Surprisingly, it is found that although the full-gap feature in the nearest-neighbor chiral $d+id$ pairing is robust, the next-nearest-neighbor $d+id$ state shows a doping-dependent gap anisotropy with a crossover from a U-shaped to a V-shaped gap profile. This gap anisotropy can naturally explain the close-to-nodal gap features observed by experiments if it is not in the nodal d-wave pairing channel. (paper)