Competing effects of Hund's splitting and symmetry-breaking perturbations on electronic order in Pb$_{1-x}$Sn$_{x}$Te

TL;DR

This paper investigates how Hund's splitting and symmetry-breaking perturbations influence surface superconductivity in the topological insulator Pb$_{1-x}$Sn$_{x}$Te, revealing the stabilizing role of multiorbital effects against external magnetic fields.

Contribution

It demonstrates that Hund's splitting enhances the robustness of surface superconductivity against external magnetization in Pb$_{1-x}$Sn$_{x}$Te, highlighting the importance of multiorbital interactions.

Findings

Hund's splitting requires larger magnetization to suppress superconductivity.

Without Hund's splitting, even small magnetization destroys superconductivity.

Multiorbital effects stabilize surface electronic order.

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.