We report on novel superconducting characteristics of the heavy fermion (HF) superconductor CePt3Si without inversion symmetry through 195Pt-NMR study on a single crystal with T_c= 0.46 K that is lower than T_c= 0.75 K for polycrystals. We show that the intrinsic superconducting characteristics inherent to CePt3Si can be understood in terms of the unconventional strong-coupling state with a line-node gap below T_c= 0.46 K. The mystery about the sample dependence of T_c is explained by the fact that more or less polycrystals and single crystals inevitably contain some disordered domains, which exhibit a conventional BCS s-wave superconductivity (SC) below 0.8 K. In contrast, the Neel temperature T_N= 2.2 K is present regardless of the quality of samples, revealing that the Fermi surface responsible for SC differ from that for the antiferromagnetic order. These unusual characteristics of CePt3Si can be also described by a multiband model; in the homogeneous domains, the coherent HF bands are responsible for the unconventional SC, whereas in the disordered domains the conduction bands existing commonly in LaPt3Si may be responsible for the conventional s-wave SC. We remark that some impurity scatterings in the disordered domains break up the 4f-electrons-derived coherent bands but not others. In this context, the small peak in 1/T_1 just below T_c reported in the previous paper (Yogi et al, 2004) is not due to a two-component order parameter composed of spin-singlet and spin-triplet Cooper pairing states, but due to the contamination of the disorder domains which are in the s-wave SC state.
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