Reexamining Ginzburg-Landau theory for neutron ${}^3{P}_2$ superfluidity in neutron stars

Abstract

The Ginzburg-Landau (GL) effective theory is a useful tool to study a superconductivity or superfluidity near the critical temperature, and usually the expansion up to the 4th order in terms of order parameters is sufficient for the description of the second-order phase transition. In this paper, we discuss the GL equation for the neutron ${}^3{P}_2$ superfluidity relevant for interior of neutron stars. We derive the GL expansion up to the 8th order in the condensates and find that this order is necessary for the system to have the unique ground state, unlike the ordinary cases. Starting from the $LS$ potential, which provides the dominant attraction between two neutrons at the high density, we derive the GL equation in the path-integral formalism, where the auxiliary field method and the Nambu-Gor'kov representation are used. We present the detailed description for the trace calculation necessary in the derivation of the GL equation. As numerical results, we show the phase diagram of the neutron ${}^3{P}_2$ superfluidity on the plane spanned by the temperature and magnetic field, and find that the 8th order terms lead to a first-order phase transition, whose existence was predicted in the Bogoliubov-de Gennes equation but has not been found thus far within the framework of the GL expansion up to the 6th order.The first-order phase transition will affect the interior structures inside the neutron stars.

23 pages, 3 figures

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• Domain walls in neutron ${}^3{P}_2$ superfluids in neutron stars
• Critical endpoint and universality class of neutron ${}^3{P}_2$ superfluids in neutron stars
• Non-Abelian Half-Quantum Vortices in ${}^3{P}_2$ Topological Superfluids
• Topological confinement of vortices in two-flavor dense QCD
• Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors
• Coexistence phase of ${}^1{S}_0$ and ${}^3{P}_2$ superfluids in neutron stars
• Topological defects at the boundary of neutron ${}^3{P}_2$ superfluids in neutron stars
• 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
• Alice meets Boojums in neutron stars: vortices penetrating two-flavor quark-hadron continuity
• Proximity effects of vortices in neutron ${}^3{P}_2$ superfluids in neutron stars: Vortex core transitions and covalent bonding of vortex molecules
• Vector-boson condensates, spin-triplet superfluidity of paired neutral and charged fermions, and $3P_2$ pairing of nucleons
• 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