Title: Competing effects of Hund's splitting and symmetry-breaking perturbations on electronic order in Pb$_{1-x}$Sn$_{x}$Te,
Abstract: We study the effect of a uniform external magnetization on p-wave
superconductivity on the (001) surface of the crystalline topological
insulator(TCI) Pb$_{1-x}$Sn$_{x}$Te. It was shown by us in an earlier work that
a chiral p-wave finite momentum pairing (FFLO) state can be stabilized in this
system in the presence of weak repulsive interparticle interactions. In
particular, the superconducting instability is very sensitive to the Hund's
interaction in the multiorbital TCI, and no instabilities are found to be
possible for the "wrong" sign of the Hund's splitting. Here we show that for a
finite Hund's splitting of interactions, a significant value of the external
magnetization is needed to degrade the surface superconductivity, while in the
absence of the Hund's interaction, an arbitrarily small external magnetization
can destroy the superconductivity. This implies that multiorbital effects in
this system play an important role in stabilizing electronic order on the
surface.