Enhancement of the superconducting transition temperature due to multiband effect in the topological nodal-line semimetal Pb$_{1-x}$Sn$_{x}$TaSe$_{2}$

We report a systematic study of the normal-state and superconducting properties of single crystal Pb$_{1-x}$Sn$_{x}$TaSe$_{2}$ $(0\leq x \leq 0.23)$. Sn doping enhances the superconducting temperature $T_{c}$ up to 5.1 K while also significantly increasing impurity scattering in the crystals. For $x=0$ and 0.018, the specific heat jump at $T_{c}$ exceeds the Bardeen-Cooper-Schrieffer (BCS) weak-coupling value of 1.43, indicating the realization of strong-coupling superconductivity in undoped and slightly Sn-doped PbTaSe$_{2}$. Substituting Pb with more Sn lowers the specific heat jump at $T_{c}$ below the BCS value of 1.43, which cannot be explained by a single-gap model. Rather, the observed specific heat data of moderately Sn-doped PbTaSe$_{2}$ ($x= 0.08$ and 0.15) are reproduced by a two-gap model. Our density functional theory calculations suggest that three-dimensional Fermi pockets appear due to a reduction of the spin-orbit gap with Sn doping, and the multiband effect arising from these emergent Fermi pockets enhances the effective electron-phonon coupling strength, leading to the increase in $T_{c}$ of Pb$_{1-x}$Sn$_{x}$TaSe$_{2}$.