$^3P_2$ Superfluids Are Topological

TL;DR

This paper investigates the topological properties of $^3P_2$ superfluids, revealing various protected gapless fermions and phase behaviors relevant to neutron star cores and superconductors.

Contribution

It provides a comprehensive topological classification of $^3P_2$ superfluid phases and explores their thermodynamic stability and surface states.

Findings

Different superfluid phases host distinct topologically protected fermions.

Biaxial nematic phases are favored under magnetic fields in weak coupling.

A tricritical point may exist in neutron star cores, affecting phase transitions.

Abstract

We clarify topology of $^3P_2$ superfluids which are expected to be realized in the inner cores of neutron stars and cubic odd-parity superconductors. $^3P_2$ phases include uniaxial/biaxial nematic phases and nonunitary ferromagnetic and cyclic phases. We here show that all the phases are accompanied by different types of topologically protected gapless fermions: Surface Majorana fermions in nematic phases and a quartet of (single) itinerant Majorana fermions in the cyclic (ferromagnetic) phase. Using the superfluid Fermi liquid theory, we also demonstrate that dihedral-two and -four biaxial nematic phases are thermodynamically favored in the weak coupling limit under a magnetic field. It is shown that the tricritical point exists on the phase boundary between these two phases and may be realized in the core of realistic magnetars. We unveil the intertwining of symmetry and topology behind mass acquisition of surface Majorana fermions in nematic phases.