Interplay of charge density wave and multiband superconductivity in 2$H$-Pd$_x$TaSe$_2$

2$H$-TaSe$_2$ has been one of unique transition metal dichalcogenides exhibiting several phase transitions due to a delicate balance among competing electronic ground states. An unusual metallic state at high-$T$ is sequentially followed by an incommensurate charge density wave (ICDW) state at $\approx$ 122 K and a commensurate charge density wave (CCDW) state at $\approx$ 90 K, and superconductivity at $T_{\rm{C}}\sim$0.14 K. Upon systematic intercalation of Pd ions into TaSe$_2$, we find that CCDW order is destabilized more rapidly than ICDW to indicate a hidden quantum phase transition point at $x$$\sim$0.09-0.10. Moreover, $T_{\rm{C}}$ shows a dramatic enhancement up to 3.3 K at $x$ = 0.08, $\sim$24 times of $T_{\rm{C}}$ in 2$H$-TaSe$_2$, in proportional to the density of states $N(E_F)$. Investigations of upper critical fields $H_{c2}$ in single crystals reveal evidences of multiband superconductivity as temperature-dependent anisotropy factor $γ_H$ = $H_{c2}^{ab}$/$H_{c2}^{c}$, quasi-linear increase of $H_{c2}^{c}(T)$, and an upward, positive-curvature in $H_{c2}^{ab}(T)$ near $T_{\rm{C}}$. Furthermore, analysis of temperature-dependent electronic specific heat corroborates the presence of multiple superconducting gaps. Based on above findings and electronic phase diagram vs $x$, we propose that the increase of $N(E_F)$ and effective electron-phonon coupling in the vicinity of CDW quantum phase transition should be a key to the large enhancement of $T_{\rm{C}}$ in Pd$_x$TaSe$_2$.

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