  The existence of edge states and zero energy modes in vortex cores is a
hallmark of topologically nontrivial phases realized in various condensed
matter systems such as the fractional quantum Hall states, p+ip
superconductors, and Z_2 insulators (quantum spin Hall state). We examine this
scenario for two dimensional noncentrosymmetric superconductors which allow the
parity-mixing of Cooper pairs. It is found that even when the s-wave pairing
gap is nonzero, provided that the superconducting gap of spin-triplet pairs is
larger than that of spin-singlet pairs, gapless edge states and zero energy
Majorana modes in vortex cores emerge, characterizing topological order.
Furthermore, it is shown that for Rashba superconductors, the quantum spin Hall
effect produced by gapless edge states exists even under an applied magnetic
field which breaks time-reversal symmetry provided that the field direction is
perpendicular to the propagating direction of the edge modes. This result
making a sharp contrast to the Z_2 insulator is due to an accidental symmetry
inherent in the Rashba model. It is also demonstrated that in the case with
magnetic fields, the non-Abelian statistics of vortices is possible under a
particular but realistic condition.
