Motivated by the recent experiment indicating that superconductivity in the
doped topological insulator CuxBi2Se3 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 Tc, 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.Comment: 4+ pages, 2 figures; 20 pages suppl mat + 4 figures; published
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