Kinetic Theory for Response and Transport in Non-centrosymmetric Superconductors

We formulate a kinetic theory for non-centrosymmetric superconductors at low temperatures in the clean limit. The transport equations are solved quite generally in spin- and particle-hole (Nambu) space by performing first a transformation into the band basis and second a Bogoliubov transformation to the quasiparticle-quasihole phase space. Our result is a particle-hole-symmetric, gauge-invariant and charge conserving description, which is valid in the whole quasiclassical regime (\(|{\user2{q}}|\ll k_F\;\hbox{and}\;\hbar \omega \ll E_{\rm F}\)). We calculate the current response, the specific heat capacity, and the Raman response function. For the Raman case, we investigate within this framework the polarization dependence of the electronic (pair-breaking) Raman response for the recently discovered non-centrosymmetric superconductors at zero temperature. Possible applications include the systems CePt\(_3\)Si and Li\(_2\)Pd\(_x\)Pt\(_{3-x}\)B, which reflect the two important classes of the involved spin-orbit coupling. We provide analytical expressions for the Raman vertices for these two classes and calculate the polarization dependence of the electronic spectra. We predict a two-peak structure and different power laws with respect to the unknown relative magnitude of the singlet and triplet contributions to the superconducting order parameter, revealing a large variety of characteristic fingerprints of the underlying condensate.