  Superconductivity is observed with critical temperature $T_{c}$ = 2.0 K in
self-flux-grown single crystals of $CaBi_{2}$. This material adopts the
$ZrSi_{2}$ structure type with lattice parameters a = 4.696(1) $\AA$, b =
7.081(2) $\AA$ and c = 4.611(1) $\AA$. The crystals of $CaBi_{2}$ were studied
by means of magnetic susceptibility, specific heat and electrical resistivity
measurements. The heat capacity jump at $T_{c}$ is $\Delta C/\gamma T_{c}$ =
1.41, confirming bulk superconductivity; the Sommerfeld coefficient $\gamma$ =
4.1 $mJ\: mol^{-1}\, K^{-2}$ and the Debye temperature $\Theta_{D}$ = 157 K.
The electron-phonon coupling strength is $\lambda_{el-ph}$ = 0.59, and the
thermodynamic critical field $H_{c}$ is low, between 111 and 124 Oe $CaBi_{2}$
is a moderate coupling type-I superconductor. Results of electronic structure
calculations are reported and charge densities, electronic bands, densities of
states and Fermi surfaces are discussed, focusing on the effects of
spin\textendash orbit coupling and electronic property anisotropy. We find a
mixed quasi-2D + 3D character in the electronic structure, which reflects the
layered crystal structure of the material.
