The crystal structure, superconducting properties, and electronic structure of a novel superconducting 122-type antimonide, BaPt$_2$Sb$_2$, have been investigated by measurements of powder X-ray diffraction patterns, electrical resistivity, ac magnetic susceptibility, specific heat as well as ab-initio calculations. This material crystallizes in a new-type of monoclinic variant of the CaBe$_2$Ge$_2$-type structure, in which Pt$_2$Sb$_2$ layers consisting of PtSb$_4$ tetrahedra and Sb$_2$Pt$_2$ layers consisting of SbPt$_4$ tetrahedra are stacked alternatively and Ba atoms are located between the layers. Measurements of electrical resistivity, ac magnetic susceptibility and specific heat revealed that BaPt$_2$Sb$_2$ is a superconducting material with a $T_{rm c}$ of 1.8 K. The electronic heat capacity coefficient $gamma_{rm n}$ and Debye temperature $theta_{rm D}$ were 8.6(2) mJ/mol K$^2$ and 146(4) K, where the figures in parentheses represent the standard deviation. The upper critical field $mu_{rm 0}H_{rm c2}(0)$ and the Ginzburg-Landau coherent length $xi(0)$ were determined to be 0.27 T and 35 nm. Calculations showed that it has two three-dimensional Fermi surfaces (FSs) and two two-dimensional FSs, leading to anisotropic transport properties. The d-states of the Pt atoms in the Pt2Sb2 layers mainly contribute to $N(E_{rm F})$. A comparison between experimental and calculated results indicates that BaPt$_2$Sb$_2$ is a superconducting material with moderate coupling.
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