TY - JOUR

T1 - Topological defects at the boundary of neutron P2 3 superfluids in neutron stars

AU - Yasui, Shigehiro

AU - Chatterjee, Chandrasekhar

AU - Nitta, Muneto

N1 - Funding Information:
We would like to thank Michikazu Kobayashi and Takeshi Mizushima for discussions. This work is supported by the Ministry of Education, Culture, Sports, Science (MEXT) Supported Program for the Strategic Research Foundation at Private Universities “Topological Science” (Grant No. S1511006). This work is also supported in part by JSPS Grants-in-Aid for Scientific Research [KAKENHI Grants No. 17K05435 (S.Y.), No. 19K14713 (C.C.), No. 16H03984 (M.N.), and No. 18H01217 (M.N.)], and also by MEXT KAKENHI Grant-in-Aid for Scientific Research on Innovative Areas “Topological Materials Science” No. 15H05855 (M.N.).
Publisher Copyright:
© 2020 American Physical Society.

PY - 2020/2

Y1 - 2020/2

N2 - We study surface effects of neutron P23 superfluids in neutron stars. P23 superfluids are in uniaxial nematic (UN), D2 biaxial nematic (BN), or D4 BN phase, depending on the strength of magnetic fields from small to large. We suppose a neutron P23 superfluid in a ball with a spherical boundary. Adopting a suitable boundary condition for P23 condensates, we solve the Ginzburg-Landau equation to find several surface properties for the neutron P23 superfluid. First, the phase on the surface can be different from that of the bulk, and symmetry restoration or breaking occurs in general on the surface. Second, the distribution of the surface energy density has an anisotropy depending on the polar angle in the sphere, which may lead to the deformation of the geometrical shape of the surface. Third, the order parameter manifold induced on the surface, which is described by two-dimensional vector fields induced on the surface from the condensates, allows topological defects (vortices) on the surface, and there must exist such defects even in the ground state thanks to the Poincaré-Hopf theorem: although the numbers of the vortices and antivortices depend on the bulk phases, the difference between them is topologically invariant (the Euler number χ=2) irrespective of the bulk phases. These vortices, which are not extended to the bulk, are called boojums in the context of liquid crystals and helium-3 superfluids. The surface properties of the neutron P23 superfluid found in this paper may provide us useful information to study neutron stars.

AB - We study surface effects of neutron P23 superfluids in neutron stars. P23 superfluids are in uniaxial nematic (UN), D2 biaxial nematic (BN), or D4 BN phase, depending on the strength of magnetic fields from small to large. We suppose a neutron P23 superfluid in a ball with a spherical boundary. Adopting a suitable boundary condition for P23 condensates, we solve the Ginzburg-Landau equation to find several surface properties for the neutron P23 superfluid. First, the phase on the surface can be different from that of the bulk, and symmetry restoration or breaking occurs in general on the surface. Second, the distribution of the surface energy density has an anisotropy depending on the polar angle in the sphere, which may lead to the deformation of the geometrical shape of the surface. Third, the order parameter manifold induced on the surface, which is described by two-dimensional vector fields induced on the surface from the condensates, allows topological defects (vortices) on the surface, and there must exist such defects even in the ground state thanks to the Poincaré-Hopf theorem: although the numbers of the vortices and antivortices depend on the bulk phases, the difference between them is topologically invariant (the Euler number χ=2) irrespective of the bulk phases. These vortices, which are not extended to the bulk, are called boojums in the context of liquid crystals and helium-3 superfluids. The surface properties of the neutron P23 superfluid found in this paper may provide us useful information to study neutron stars.

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U2 - 10.1103/PhysRevC.101.025204

DO - 10.1103/PhysRevC.101.025204

M3 - Article

AN - SCOPUS:85082772884

VL - 101

JO - Physical Review C

JF - Physical Review C

SN - 2469-9985

IS - 2

M1 - 025204

ER -