TY - JOUR

T1 - Reexamining Ginzburg-Landau theory for neutron P2 3 superfluidity in neutron stars

AU - Yasui, Shigehiro

AU - Chatterjee, Chandrasekhar

AU - Kobayashi, Michikazu

AU - Nitta, Muneto

N1 - Funding Information:
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). C.C. acknowledges support as an International Research Fellow of the Japan Society for the Promotion of Science (JSPS) (Grant No. 16F16322). This work is also supported in part by JSPS Grant-in-Aid for Scientific Research [KAKENHI Grant No. 16H03984 (M.N.), No. 18H01217 (M.N.), No. 17K05435 (S.Y.), and No. 19K14713 (C.C.)] and also by MEXT KAKENHI Grant-in-Aid for Scientific Research on Innovative Areas “Topological Materials Science” [Grant No. 15H05855 (M.N.)].
Publisher Copyright:
© 2019 American Physical Society.

PY - 2019/8/5

Y1 - 2019/8/5

N2 - 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 fourth-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 P23 superfluidity relevant for interior of neutron stars. We derive the GL expansion up to the eighth 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 P23 superfluidity on the plane spanned by the temperature and magnetic field, and we find that the eighth-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 sixth order. The first-order phase transition will affect the interior structures inside the neutron stars.

AB - 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 fourth-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 P23 superfluidity relevant for interior of neutron stars. We derive the GL expansion up to the eighth 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 P23 superfluidity on the plane spanned by the temperature and magnetic field, and we find that the eighth-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 sixth order. The first-order phase transition will affect the interior structures inside the neutron stars.

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U2 - 10.1103/PhysRevC.100.025204

DO - 10.1103/PhysRevC.100.025204

M3 - Article

AN - SCOPUS:85070561113

VL - 100

JO - Physical Review C

JF - Physical Review C

SN - 2469-9985

IS - 2

M1 - 025204

ER -