  Recently the superconductor and topological semimetal PbTaSe$_2$ was
experimentally found to exhibit surface-only lattice rotational symmetry
breaking below $T_c$. We exploit the Ginzburg-Landau free energy and propose a
microscopic two-channel model to study possible superconducting states on the
surface of PbTaSe$_2$. 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 find that such
time-reversal symmetry breaking is unavoidable for a superconducting state in a
two dimensional irreducible representation of crystal point group in a system
where the spatial inversion symmetry is broken and the strong spin-orbit
coupling is present. Our findings will guide the search for topological chiral
superconductors.
