  Superconducting properties of hypothetical simple hexagonal CaB2 are studied
using the fully anisotropic Eliashberg formalism based on electronic and
phononic structures and electron-phonon interactions which are obtained from ab
initio pseudopotential density functional calculations. The superconducting
transition temperature Tc, the superconducting energy gap Delta(k) on the Fermi
surface, and the specific heat are obtained and compared with corresponding
properties of MgB2. Our results suggest that CaB2 will have a higher Tc and a
stronger two-gap nature, with a larger Delta(k) in the sigma bands but a
smaller Delta(k) in the pi bands than MgB2.
