  Motivated by the recent experiment indicating that superconductivity in the
doped topological insulator Cu$_x$Bi$_2$Se$_3$ has an odd-parity pairing
symmetry with rotational symmetry breaking, we study the general class of
odd-parity superconductors with two-component order parameters in trigonal and
hexagonal crystal systems. In the presence of strong spin-orbit interaction, we
find two possible superconducting phases below $T_c$, a time-reversal-breaking
(i.e., chiral) phase and an anisotropic (i.e., nematic) phase, and determine
their relative energetics from the gap function in momentum space. The nematic
superconductor generally has a full quasi-particle gap, whereas the chiral
superconductor with a three-dimensional (3D) Fermi surface has point nodes with
lifted spin degeneracy, resulting in itinerant Majorana fermions in the bulk
and topological Majorana arcs on the surface.
