Specific-heat study for the coupling between two superconducting order parameters in Na$_{x}$Mn$_{z}$Co$_{1-z}$O$_{2}$·yH$_{2}$O.

The substitution of Mn doping into the Co site, has been confirmed by the Mn $L$-edge XANES and EXAFS spectra, is performed by the specific-heat measurement with and without magnetic field. Due to the possible coexistence of isotropic and nodal-line gap, the two superconducting order parameters should exhibit different $T_{c}$ suppression rate by the doping impurity. Without field, two anomalies are seen below $T_{c}$, $\sim $ 4 K determined from magnetization, may be caused by different superconducting contributions due to the impurity effect and then merge into one under higher magnetic field ($\sim $1T). Schottky effect needs to be taken into account in the normal state.