  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.
