Superfluid Band Theory for the Rod Phase in the Magnetized Inner Crust Matter: Entrainment, Spin-orbit Coupling, Spin-triplet Pairing

TL;DR

This paper develops a theoretical framework for the superfluid band structure in the magnetized inner crust of neutron stars, revealing how strong magnetic fields influence neutron effective mass, pairing, and spin polarization in two-dimensional rod-phase matter.

Contribution

It introduces a comprehensive model incorporating band-structure, spin-triplet pairing, and magnetic effects in the neutron star crust, highlighting the role of spin-orbit interaction and magnetic-field-induced spin polarization.

Findings

Magnetic fields of 10^{16} G enhance neutron effective mass by ~1.5 times.

Spin-orbit interaction induces spin polarization under magnetic fields.

Rank-0 superfluid component emerges from magnetic polarization, rank-2 depends on pairing interactions.

Abstract

The inner crust of neutron stars hosts a rich variety of nuclear phenomena and provides a unique environment for exploring microscopic nuclear properties relevant to diverse astrophysical observations. Particularly magnetars, which possess extremely strong magnetic-fields, have attracted increasing attention in connection with nuclear spin dynamics and unconventional pairing correlations. This work is dedicated to develop a comprehensive theoretical framework to describe the structures and properties of two-dimensional (rod-phase) matter in the neutron star inner crust, incorporating band-structure effects, neutron spin-triplet pairing, and strong magnetic-fields on an equal footing. The main results of this study can be summarized as follows. In the first place, the magnetic-fields of the order of $10^{16}\,$G are found to substantially enhance the neutron effective mass by a factor of approximately $1.5$, indicating a significant modification of entrainment properties in strongly magnetized crustal matter. In the second place, while the overall behavior of pairing phase transitions is qualitatively similar to that observed in one-dimensional systems studied previously, the present two-dimensional calculations reveal a nontrivial role of the spin-orbit interaction in inducing spin-polarization under magnetic fields. In the third place, concerning spin-triplet superfluidity, the rank-0 component is shown to emerge as a consequence of magnetic-field-induced spin-polarization, irrespective of the presence of spin-triplet pairing interactions, whereas the rank-2 component appears only when the corresponding interaction channel is included.