Unusual superconductivity in the topological nodal-line semimetal candidate Sn$x$NbSe${2-δ}$

Topological superconductivity has attracted great interest because of the potential of Majorana fermions for technological application. One of the promising candidates for topological superconductors is noncentrosymmetric superconductors with strong spin-orbit coupling. The lack of centrosymmetry can induce an odd-parity pairing state, which is a prerequisite of topological superconductivity. Among such noncentrosymmetric systems, the topological nodal-line semimetal PbTaSe$_2$ shows superconductivity at 3.8 K [1], and its superconducting gap exhibits nematic behavior [2], similar to metal-intercalated Bi$_2$Se$_3$ [3]. In addition, a member of the PbTaSe$_2$ family, SnNbSe$_2$, is theoretically predicted to be a topological nodal-line semimetal and a superconductor [4]. The calculated superconducting transition temperature of this compound is 7 K, relatively higher than most of the known topological superconductor candidates. We here report the superconductivity of Sn$_x$NbSe$_{2-\delta}$ with the same noncentrosymmetric structure as stoichiometric SnNbSe$_2$. The superconducting transition temperature $T_c$ of Sn$_x$NbSe$_{2-\delta}$ drastically varies with the Sn concentration $x$ and the Se deficiency $\delta$. The upper critical field of this material shows unusual temperature dependence, inconsistent with the WHH theory for conventional type-II superconductors. Moreover, the zero-temperature limit of the upper critical field of Sn$_x$NbSe$_{2-\delta}$ with low $T_c$ exceeds the Pauli paramagnetic limit estimated from the simple BCS weak coupling model, suggestive of unusual superconductivity stabilized in Sn$_x$NbSe$_{2-\delta}$. We will also report the correlation between the superconducting transition temperatures and carrier densities of this system.