Transport Properties and Electronic Phase Diagram of Single-Crystalline Ca$_{10}$(Pt$_3$As$_8$) ((Fe$_{1-x}$Pt$_x$)$_2$As$_2$)$_5$

Sizable single-crystalline samples of Ca$_{10}$(Pt$_3$As$_8$)((Fe$_{1-x}$Pt$_x$)$_2$As$_2$)$_5$ (the 10-3-8 phase) with 0$\leq x<$0.1 have been grown and systematically characterized via X-Ray diffraction, magnetic, and transport measurements. The undoped sample is a heavily doped semiconductor with no sign of magnetic order down to 2 K. With increasing Pt content, the metallic behavior appears and superconductivity is realized for $x\geq$0.023. $T_{\rm c}$ rises to its maximum of approximately 13.6 K at the doping level of $x\sim$0.06, and then decreases for higher $x$ values. The electronic phase diagram of the 10-3-8 phase was mapped out based on the transport measurements. The mass anisotropy parameter $\Gamma\sim$10 obtained from resistive measurements in magnetic fields indicates a relatively large anisotropy in the iron-based superconductor family. This strong 2D character may lead to the absence of magnetic order. A linear $T$-dependence of susceptibility at high temperature is observed, indicating that spin fluctuations exist in the underdoped region as in most of the Fe-pnictide superconductors.