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Strong coupling effects on the upper critical fields $H_{c2}$ along thec-axis in the noncentrosymmetric heavy fermion superconductors near quantumcriticality CeRhSi$_3$ and CeIrSi$_3$ are examined. For sufficiently largespin-orbit interactions due to the lack of inversion symmetry, $H_{c2}$ ismainly determined by the orbital depairing effects. From microscopiccalculations taking into account the strong spin fluctuations, we show that$H_{c2}$ is extremely enhanced as the system approaches the quantum criticalpoint, resulting in $H_{c2}\sim 30$T even in the case with the low transitiontemperature $T_c(H=0)\sim 1$K, which well explains the huge $H_{c2}$ observedin the recent experiments. Our results reveal intrinsic and universalproperties common to strong coupling superconductivity caused by spinfluctuations near quantum criticality.

physical review letters

Colossal enhancement of upper critical fields in noncentrosymmetric  heavy fermion superconductors near quantum criticality: CeRhSi$_3$ and  CeIrSi$_3$