Microscopic description of axisymmetric vortices in $^{3}$P$_{2}$ superfluids

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 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.