The heavy fermion compound CeRhIn 5 is a rare example where a quantum critical point, hidden by a dome of superconductivity, has been explicitly revealed and found to have a local nature. The lack of additional examples of local types of quantum critical points associated with superconductivity, however, has made it difficult to unravel the role of quantum fluctuations in forming Cooper pairs. Here, we show the precise control of superconductivity by tunable quantum critical points in CeRhIn 5 . Slight tin-substitution for indium in CeRhIn 5 shifts its antiferromagnetic quantum critical point from 2.3 GPa to 1.3 GPa and induces a residual impurity scattering 300 times larger than that of pure CeRhIn 5 , which should be sufficient to preclude superconductivity. Nevertheless, superconductivity occurs at the quantum critical point of the tin-doped metal. These results underline that fluctuations from the antiferromagnetic quantum criticality promote unconventional superconductivity in CeRhIn 5 .

We report the pressure response of charge-density-wave (CDW) and ferromagnetic (FM) phases of the rare-earth intermetallic SmNiC2 up to 5.5 GPa. The CDW transition temperature (TCDW ), which is reflected as a sharp inflection in the electrical resistivity, is almost independent of pressure up to 2.18 GPa but is strongly enhanced at higher pressures, increasing from 155.7 K at 2.2 GPa to 279.3 K at 5.5 GPa. Commensurate with the sharp increase in TCDW , the first-order FM phase transition, which decreases with applied pressure, bifurcates into the upper (TM1) and lower (Tc) phase transitions and the lower transition changes its nature to second order above 2.18 GPa. Enhancement both in the residual resistivity and the Fermi-liquid T 2 coefficient A near 3.8 GPa suggests abundant magnetic quantum fluctuations that arise from the possible presence of a FM quantum critical point. Low dimensional metallic systems have attracted much interest because of their propensity towards an ordered phase. Density waves are prominent examples in quasione-dimensional compounds, where a large anisotropy in the Fermi surface leads to a structural instability accompanied by a periodic lattice distortion 1 . Sensitivity to the Fermi surface topology makes it relatively easy to tune the ordered phases via such external parameters as chemical doping, pressure, and magnetic fields. For the transition-metal dichalcogenide TiSe 2 , a CDW transition temperature is suppressed with increasing Cu intercalation and is intercepted by a dome of superconductivity centered around a projected critical concentration where the extrapolated T CDW becomes zero.2 External pressure acts similarly to suppress the CDW phase of TiSe 2 , inducing superconductivity in the vicinity of a projected CDW critical point.3 These results both by Cu intercalation and external pressure suggest that correlated electrons spontaneously adjust to a new emergent phase in the vicinity of a quantum critical point.Rare-earth intermetallic compounds ReNiC 2 (Re =La, Ce, Nd, Sm, Gd, Tb, Er) show various ground states of CDWs and magnetism.4,5 Among the intermetallics, SmNiC 2 is unique in that it becomes ferromagnetic, while other members are prone to an antiferromagnetic instability. X-ray scattering studies of SmNiC 2 reveal satellite peaks corresponding to an incommensurate wave vector (0.5, 0.52, 0) below 148 K, signaling formation of a charge-density wave.6 The abrupt disappearance of the satellite peak at the ferromagnetic transition temperature (T c = 17.4 K) indicates a destruction of the CDW phase and a strong correlation between the FM and CDW phases. First-principles electronic structure calculations find that Fermi-surface nesting is important for the CDW state and weaker nesting in the ferromagnetic phase leads to the destruction of the CDW below T c (ref. 7). Kim et al. recently estimated that hydrostatic pressure will enhance the CDW because the lattice constant of the Ni chain along the a-axis decreases faster than other axes, thus enhancing the Fermi surface nes...

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