Nonunitary spin-triplet superconductors in Zeeman magnetic field

Abstract: We study spin-triplet superconductivity with both unitary and nonunitary pairing in the presence of an external Zeeman magnetic field. Within a mean-field framework, we exactly diagonalize the Bogoliubov-de Gennes Hamiltonian and derive general expressions for the quasiparticle spectrum, superconducting gap, critical temperature, and spin magnetization, valid for arbitrary magnetic-field strengths and temperatures. We analyze in detail the nonlinear spin susceptibility and the field evolution of the superconducting gap and transition temperature, highlighting qualitative differences between unitary and nonunitary pairing states. Our results are broadly applicable to a wide range of materials, including systems with both weak and strong spin-orbit coupling. We show that systematic measurements of the critical temperature and spin susceptibility as functions of the magnitude and orientation of the magnetic field provide a powerful means to identify the structure of the spin-triplet order parameter, and we discuss implications of our findings for candidate materials such as 4Hb-TaS$2$ and PrOs$_4$Sb${12}$.