We report on high-pressure (p_max = 2.1 GPa) muon spin rotation experiments probing the temperature-dependent magnetic penetration depth in the layered superconductor 2H-NbSe_2. Upon increasing the pressure, we observe a substantial increase of the superfluid density n_s, which we find to scale linearly with T_c. This linear scaling is considered a hallmark feature of unconventional superconductivity, especially in high-temperature cuprate superconductors. Our current results, along with our earlier findings on 1T-MoTe_2 (Z. Guguchia et. al., Nature Communications 8, 1082 (2017)), demonstrate that this linear relation is also an intrinsic property of the superconductivity in transition metal dichalcogenides, whereas the ratio T_c/T_F is approximately a factor of 20 lower than the ratio observed in hole-doped cuprates. We, furthermore, find that the values of the superconducting gaps are insensitive to the suppression of the quasi-two-dimensional CDW state, indicating that the CDW ordering and the superconductivity in 2H-NbSe_2 are independent of each other.
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