We report an in-depth Angle Resolved Photoemission Spectroscopy (ARPES) study on $2H$-TaS$_2$, a canonical incommensurate Charge Density Wave (CDW) system. This study demonstrates that just as in related incommensurate CDW systems, $2H$-TaSe$_2$ and $2H$-NbSe$_2$, the energy gap ($Delta_{text{cdw}},$) of $2H$-TaS$_2$ is localized along the K-centered Fermi surface barrels and is particle-hole asymmetric. The persistence of $Delta_{text{cdw}},$ even at temperatures higher than the CDW transition temperature $it{T}_{text{cdw}},$ in $2H$-TaS$_2$, reflects the similar pseudogap (PG) behavior observed previously in $2H$-TaSe$_2$ and $2H$-NbSe$_2$. However, in sharp contrast to $2H$-NbSe$_2$, where $Delta_{text{cdw}},$ is non-zero only in the vicinity of a few hot spots on the inner K-centered Fermi surface barrels, $Delta_{text{cdw}},$ in $2H$-TaS$_2$ is non-zero along the entirety of both K-centered Fermi surface barrels. Based on a tight-binding model, we attribute this dichotomy in the momentum dependence and the Fermi surface specificity of $Delta_{text{cdw}},$ between otherwise similar CDW compounds to the different orbital orientations of their electronic states that are involved in CDW pairing. Our results suggest that the orbital selectivity plays a critical role in the description of incommensurate CDW materials.
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