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The CuIr 2−x Ru x Te 4 superconductors (with a T c around 2.8 K) can host charge-density waves, whose onset and interplay with superconductivity are not well known at a microscopic level. Here, we report a comprehensive study of the x = 0 and 0.05 cases, whose superconductivity was characterized via electrical-resistivity, magnetization, and heat-capacity measurements, while their microscopic superconducting properties were studied via muon-spin rotation and relaxation (μSR). In CuIr 2−x Ru x Te 4 , both the temperature-dependent electronic specific heat and the superfluid density (determined via transverse-field μSR) are best described by a two-gap (s + d)-wave model, comprising a nodeless gap and a gap with nodes. The multigap superconductivity is also supported by the temperature dependence of the upper critical field H c2 (T ). However, under applied pressure, a charge-density-wave order starts to develop and, as a consequence, the superconductivity of CuIr 2 Te 4 achieves a more conventional s-wave character. Our series of experiments provides ample evidence that the CuIr 2−x Ru x Te 4 family belongs to the rare cases where an unconventional superconducting pairing is found near a charge-density-wave quantum critical point.

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