Superconductivity in materials without inversion symmetry reveals intriguing properties, since a strong antisymmetric spin-orbit coupling (ASOC) splits the Fermi surface and invalidates the classification of the superconducting order parameter with respect to spin singlet/even parity and spin triplet/odd parity. This, in turn, allows unconventional Cooper-pairing in a so-called mixed parity form which is a linear combination of both spin singlet and spin triplet on the splitted bands. Since the g-vector of the ASOC and the d-vector of the triplet state turn out to be parallel, the resulting order parameter reads:
Δk± = Ψ ± d|gk| = Ψ(1±p|gk|) = Δ±
where the parameter p = d / Ψ represents the unknown triplet-singlet ratio. In order to analyze the so-called mixed parity form we have formulated a kinetic theory for low temperatures and in the clean limit. The transport equations are solved in three dimensions for any kind of ASOC in an extended momentum and frequency range. Our result is a particle-hole symmetric, gauge-invariant and charge conserving description that allows to calculate various response functions
As an application of our kinetic theory, the polarization-dependent electronic Raman response in non-centrosymmetric superconductors (NCS) is studied for two important cases of the ASOC in CePt3Si and Li2PdxPt3-xB. New analytical expressions for the Raman vertices are derived and the low-energy power laws as well as characteristic pair-breaking peaks are calculated. The total Raman response is a sum of both bands:
Χγγtotal = Χγγ(Δ-) + Χγγ(Δ+).
In general, we predict a two-peak structure due to both singlet and triplet contributions of the superconducting order parameter. Our predictions will help to detect the unknown relative magnitude of the singlet and triplet gap in these materials, see Fig. 3.