Coexistence phase of ${}^1{S}_0$ and ${}^3{P}_2$ superfluids in neutron stars

Abstract

In neutron star matter, there exist ${}^1{S}_0$ superfluids in lower density in the crust while ${}^3{P}_2$ superfluids are believed to exist at higher density deep inside the core. In the latter, depending on the temperature and magnetic field, either the uniaxial nematic phase, the D${}_2$-biaxial nematic phase, or the D${}_4$-biaxial nematic phase appears. In this paper, we discuss a mixture of the ${}^1{S}_0$ and ${}^3{P}_2$ superfluids and find their coexistence. Adopting the loop expansion and the weak-coupling approximation for the interaction between two neutrons, we obtain the Ginzburg-Landau (GL) free energy in which both of the ${}^1{S}_0$ and ${}^3{P}_2$ condensates are taken into account by including the coupling terms between them. We analyze the GL free energy and obtain the phase diagram for the temperature and magnetic field. We find that the ${}^1{S}_0$ superfluid excludes the ${}^3{P}_2$ superfluid completely in the absence of magnetic field, they can coexist for weak magnetic fields, and the ${}^1{S}_0$ superfluid is expelled by the ${}^3{P}_2$ superfluid at strong magnetic fields, thereby proving the robustness of ${}^3{P}_2$ superfluid against the magnetic field. We further show that the D${}_4$-BN phase covers the whole region of the ${}^3{P}_2$ superfluidity as a result of the coupling term, in contrast to the case of a pure ${}^3{P}_2$ superfluid studied before in which the D${}_4$-BN phase is realized only under strong magnetic fields. Thus, the D${}_4$-BN phase is topologically the most interesting phase, e.g., admitting half-quantized non-Abelian vortices relevant not only in magnetars but also in ordinary neutron stars.

14 pages, 3 figures

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• ${}^1$S${}_0$ pairing gaps, chemical potential and entrainment matrix in superfluid neutron-star cores for the Brussels-Montreal functionals
• Spin-polarized phases of ${}^3{P}_2$ superfluids in neutron stars
• Core structures of vortices in Ginzburg-Landau theory for neutron ${}^3{P}_2$ superfluids
• Proximity effects of vortices in neutron ${}^3{P}_2$ superfluids in neutron stars: Vortex core transitions and covalent bonding of vortex molecules
• Competition between pairing and tripling in one-dimensional fermions with coexistent s- and p-wave interactions
• Josephson currents in neutron stars
• Strongly interacting matter in extreme magnetic fields
• Symmetry classification of uniform states in spin-2 Bose-Einstein condensates and neutron ${}^3{P}_2$ superfluids
• Emergent chirality and superfluidity of parity-doubled baryons in neutron stars
• Mass-imbalance effect on the cluster formation in a one-dimensional Fermi gas with coexistent $s$- and $p$-wave interactions