# Microscopic description of axisymmetric vortices in $^{3}P_{2}$ superfluids

## TL;DR

This paper employs a microscopic approach to analyze quantized vortices in ${}^{3}P_{2}$ superfluids, revealing stable vortex configurations, Majorana bound states, and significant differences in core magnetization profiles.

## Contribution

First microscopic study of vortices in ${}^{3}P_{2}$ superfluids using Eilenberger and BdG equations, identifying stable vortex types and Majorana states.

## Key findings

- Multiple stable and metastable vortex configurations depending on magnetic field.
- The $o$ vortex is most stable under strong magnetic fields.
- Two zero-energy Majorana fermion bound states are found in the $o$ vortex core.

## Abstract

We study quantized vortices in ${}^{3}P_{2}$ superfluids using a microscopic theory for the first time. The theory is based on the Eilenberger equation to determine the order parameters and the Bogoliubov-de Gennes (BdG) equation to obtain the eigenenergies and the core magnetization. Within axisymmetric vortex configurations, we find several stable and metastable vortex configurations which depend on the strength of a magnetic field, similar to a $v$ vortex and $o$ vortex in $^3$He superfluids. We demonstrate that the $o$ vortex is the most stable axisymmetric vortex in the presence of a strong magnetic field, and we find two zero-energy Majorana fermion bound states in the $o$-vortex core. We show that the profiles of the core magnetization calculated using the BdG equation are drastically different from those calculated using only the order parameter profiles known before.