  The low-energy electronic properties of the new superconductors BaPtSb and
BaPtAs with an ordered honeycomb network are investigated in the normal phase,
where the former compound is a candidate for time-reversal symmetry-breaking
superconductors. By means of the first-principles calculation, we show that
there exist two-dimensional cylinder-like Fermi surfaces around the kz axis and
one outer spherelike Fermi surface around the K and K' points in both
compounds, which are mainly composed of Pt 5d and Sb 5p/As 4p electrons. We
construct low-energy effective models, which are well described by using three
bands consisting of two Pt 5d orbitals and one Sb 5p/As 4p orbital. By
evaluating susceptibilities using effective models, we find that dominant
contributions to those susceptibilities result from the outer spherelike Fermi
surface. Whereas out-of-plane fluctuations are enhanced in both compounds in
the higher-temperature region, in-plane fluctuations become dominant in the
very low-temperature region in BaPtSb owing to a better nesting condition in
the k_z=0 plane from the outer spherelike Fermi surface. These fluctuations
yield instabilities to ordered states, such as superconductivity, and might be
associated with the occurrence of the superconducting state with time-reversal
symmetry breaking in BaPtSb.
