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We study the normal and the superconducting properties in noncentrosymmetricheavy fermion superconductors CeRhSi$_3$ and CeIrSi$_3$. For the normal state,we show that experimentally observed linear temperature dependence of theresistivity is understood through the antiferromagnetic spin fluctuations nearthe quantum critical point (QCP) in three dimensions. For the superconductingstate, we derive a general formula to calculate the upper critical field$H_{c2}$, with which we can treat the Pauli and the orbital depairing effect onan equal footing. The strong coupling effect for general electronic structuresis also taken into account. We show that the experimentally observed featuresin $H_{c2}\parallel \hat{z}$, the huge value up to 30(T), the downwardcurvatures, and the strong pressure dependence, are naturally understood as aninterplay of the Rashba spin-orbit interaction due to the lack of inversionsymmetry and the spin fluctuations near the QCP. The large anisotropy between$H_{c2}\parallel \hat{z}$ and $H_{c2}\perp \hat{z}$ is explained in terms ofthe spin-orbit interaction. Furthermore, a possible realization of theFulde-Ferrell- Larkin-Ovchinnikov state for $H\perp \hat{z}$ is studied. Wealso examine effects of spin-flip scattering processes in the pairinginteraction and those of the applied magnetic field on the spin fluctuations.We find that the above mentioned results are robust against these effects. Theconsistency of our results strongly supports the scenario that thesuperconductivity in CeRhSi$_3$ and CeIrSi$_3$ is mediated by the spinfluctuations near the QCP.

Spin fluctuations and superconductivity in noncentrosymmetric heavy fermion systems CeRhSi$_3$ and CeIrSi$_3$