Nodal and multi-gap superconductivity in Ta$_{4}$Pd$_{3}$Te$_{16}$ with weakly ferromagnetic normal state

We recently discovered bulk superconductivity at $T_{\mathrm{c}}=$4.6 K in a transition metal telluride Ta$_{4}$Pd$_{3}$Te$_{16}$ [W. H. Jiao et al., J. Am. Chem. Soc. 136, 1284 (2014)]. This material has a layered structure with one-dimensional PdTe$_{2}$ chains. Significant electron correlations are indicated by the enhanced Sommerfeld coefficient. Here we report the measurements of magnetoresistance, Hall effect, magnetization and specific heat using high-quality crystals. Our results show that Ta$_{4}$Pd$_{3}$Te$_{16}$ is an anisotropic type-II superconductor. The anisotropy of upper critical fields $H_{\mathrm{c2}}(T)$ is strongly $T$-dependent, resulted from the multi-band effect. The zero-field electronic specific heat $C_{\mathrm{e}}(T)$ far below the $T_{\mathrm{c}}$ is found to be proportional to $T^{3}$, suggestive of presence of point nodes in at least one of the superconducting gaps, which is further supported by a nonlinear ($\propto H^{1/2})$ field dependence of Sommerfeld coefficient in the mixed state. Notably, the material shows anisotropic weak-ferromagnetism above $T_{\mathrm{c}}$, implying that spin-triplet superconductivity is likely in this material.