# Role of Hund's splitting in electronic phase competition in ${\rm Pb}_{1-x}{\rm Sn}_{x}{\rm Te}$

## TL;DR

This paper investigates how Hund's splitting influences electronic phase competition in Pb$_{1-x}$Sn$_{x}$Te near Van Hove singularities, revealing conditions that favor a chiral p-wave FFLO state through renormalization group analysis.

## Contribution

It introduces a multipatch parquet RG approach to analyze Hund's splitting effects on phase competition in a topological crystalline insulator.

## Key findings

- Chiral p-wave FFLO state is favored with antiparallel spin interactions.
- No electronic instabilities occur if fixed-point interactions do not favor antiparallel spins.
- Momentum-dependent interactions are crucial due to Berry phase effects.

## Abstract

We study the effect of Hund's splitting of repulsive interactions on electronic phase transitions in the multiorbital topological crystalline insulator Pb$_{1-x}$Sn$_{x}$Te, when the chemical potential is tuned to the vicinity of low-lying Type-II Van Hove singularities. Nontrivial Berry phases associated with the Bloch states impart momentum-dependence to electron interactions in the relevant band. We use a multipatch parquet renormalization group (RG) analysis for studying the competition of different electronic phases, and find that if the dominant fixed-point interactions correspond to antiparallel spin configurations, then a chiral $p$-wave Fulde-Ferrell-Larkin-Ovchinnikov(FFLO) state is favored, otherwise, none of the commonly encountered electronic instabilities occur within the one-loop parquet RG approach.