  Noncentrosymmetric superconductors with various types of pairing interactions
are systematically examined with particular focus on phenomena that originate
from the differences between Fermi surfaces split by a strong spin-orbit
coupling. In particular, when the spin-orbit coupling increases and one of the
split Fermi surfaces disappears, the phase diagram and the structure of the gap
function change drastically. For example, we examine the conditions for the
transition from full-gap states to line-node states (FLT), which may explain
the differences in the experimental results between the noncentrosymmetric
superconductors Li2Pd3B and Li2Pt3B discovered recently. The dominant pairing
interactions and gap functions can be predicted to some extent by comparing the
theoretical and experimental results for these compounds. For example, if the
FLT occurs by replacing Pd with Pt, it is most likely that the
superconductivity is mainly induced by charge-charge interactions, and if this
is the case, the superconductivities in Li2Pd3B and Li2Pt3B are an s-wave
nearly spin-triplet state and a d-wave state that has both spin-singlet and
triplet components of comparable weights, respectively. Comparing the
theoretical phase diagrams in simple models, it is found that the FLT occurs in
a wider realistic parameter region for charge-charge interactions, i.e., where
short-range Coulomb repulsion is strong and p-wave and d-wave interactions are
attractive, while it occurs in narrower rather unrealistic parameter regions
for interactions of magnetic origin. It is also found that d-wave spin-triplet
pairing may occur, when pairing interactions are of magnetic origin and
anisotropic in spin space.
