Materials with multiple superconducting phases are rare. Here, we report the discovery of two-phase unconventional superconductivity in CeRh2As2. Using thermodynamic probes, we establish that the superconducting critical field of its high-field phase is as high as 14 tesla, even though the transition temperature is only 0.26 kelvin. Furthermore, a transition between two different superconducting phases is observed in a c axis magnetic field. Local inversion-symmetry breaking at the cerium sites enables Rashba spin-orbit coupling alternating between the cerium sublayers. The staggered Rashba coupling introduces a layer degree of freedom to which the field-induced transition and high critical field seen in experiment are likely related.

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Superconductivity in noncentrosymmetric LaNiC 2 is expected to be induced by electron-phonon interactions due to its lack of magnetic instabilities. The non-Bardeen-Cooper-Schrieffer (BCS) behaviors found in this material call into question the long-standing idea that relates unconventional superconductivity with magnetic interactions. Here we report magnetic penetration-depth measurements in a high-purity single crystal of LaNiC 2 at pressures up to 2.5 GPa and temperatures down to 0.04 K. At ambient pressure and below 0.5T c the penetration depth goes as T 4 for the in-plane and T 2 for the out-of-plane component, firmly implying the existence of point nodes in the energy gap and the unconventional character of this superconductor. The present study also provides first evidence of magnetism in LaNiC 2 by unraveling a pressure-induced antiferromagnetic phase inside the superconducting state at temperatures below 0.5 K, with a quantum critical point around ambient pressure. The results presented here maintain a solid base for the notion that unconventional superconductivity only arises near magnetic order or fluctuations. 1 arXiv:1806.03818v1 [cond-mat.supr-con]

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