Noncentrosymmetric superconductors have sparked significant research interests due to their exciting properties, such as the admixture of spin-singlet and spin-triplet Cooper pairs. Here we report $mu$SR and thermodynamic measurements on the noncentrosymmetric superconductor La7Rh3 which indicate a fully established superconducting gap and spontaneous time-reversal-symmetry breaking at the onset of superconductivity. We show that our results pose severe constraints on any microscopic theory of superconductivity in the system. A symmetry analysis identifies ground states compatible with time-reversal-symmetry breaking and the resulting gap functions are discussed. Furthermore, general energetic considerations indicate the relevance of electron-electron interactions for the pairing mechanism, in accordance with hints of spin-fluctuations revealed in susceptibility measurements.
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