Topological Superconductivity Intertwined with Broken Symmetries

Recently the superconductor and topological semimetal PbTaSe2 was experimentally found to exhibit surface-only lattice rotational symmetry breaking below Tc . We exploit the Ginzburg-Landau free energy and propose a microscopic two-channel model to study possible superconducting states on the surface of PbTaSe2 . We identify two types of topological superconducting states. One is time-reversal invariant and preserves the lattice hexagonal symmetry while the other breaks both symmetries. We prove that for a C3v lattice with spatial inversion symmetry breaking and strong spin-orbit coupling, the time reversal symmetry must be broken and the only way to lead a nematic superconductor is the mixing of 1D and 2D irreducible representation superconducting states.