Odd-parity superconductors with two-component order parameters: nematic and chiral, gapped and nodal

Motivated by growing experimental evidence that superconductivity in the doped topological insulator CuxBi2Se3 has an odd-parity pairing with broken rotational symmetry, we study the general class of odd-parity superconductors with two-component order parameters. We address the energetics and physical properties of different superconducting phases, with special emphasis on the role of spin-orbit coupling, which is generally strong in topological insulator and related materials. We show that within the weak-coupling BCS theory, in the absence of spin-orbit coupling, isotropic superconductors are favored, which are analogs of the A- or B-phase of $^3$He. In the presence of spin-orbit coupling, however, we find that a nematic superconducting phase, which spontaneously breaks rotational symmetry are favored. We determine the superconducting gap structures and find, in addition to fully gapped odd-parity superconductors, nodal superconductors with Dirac and Weyl quasiparticles, which are markedly different from superfluid phases of $^3$He.