A revisit of superconductivity in 4$H_b$-TaS$_{2-2x}$Se$_{2x}$ single crystals

Previous investigations of 4$H_b$-TaS$_{2-2x}$Se$_{2x}$ mainly focused on the direct competition between superconductivity and charge density wave (CDW). However, the superconductivity itself, although has been prominently enhanced by isovalent Se substitution, has not been adequately investigated. Here, we performed a detailed electrical transport measurement down to 0.1 K on a series of 4$H_b$-TaS$_{2-2x}$Se$_{2x}$ single crystals. A systematic fitting of the temperature-dependent resistance demonstrates that the decreased Debye temperatures ($\Theta_{D}$) and higher electron-phonon coupling constants ($\lambda_{e-p}$) at the optimal Se doping content raise the superconducting transition temperature ($T_c$). Additionally, we discovered that the incorporation of Se diminishes the degree of anisotropy of the superconductivity in the highly layered structure. More prominently, a comprehensive analysis of the vortex liquid phase region reveals that the optimally doped sample deviates from the canonical 2D Tinkham prediction but favors a linear trend with the variation of the external magnetic field. These findings emphasize the importance of interlayer interaction in this segregated superconducting-Mott-insulating system.