Evolution and Instability of Bogoliubov Fermi Surfaces under Zeeman Field

We theoretically investigate the evolution and instability of the Bogoliubov Fermi surface (BFS) in the spherical $j=3/2$ model under a Zeeman field. The applied field induces a pronounced expansion in the BFS with $j_z = \pm 3/2$ component. Such behavior can be detected by spectroscopic techniques such as angle-resolved photoemission spectroscopy (ARPES). Interestingly, the Pauli susceptibility exhibits behavior that appears discontinuous just below the transition temperature at zero field, even though it is a second-order transition. This is due to spontaneous magnetization. Furthermore, the analysis of the bogolon correlations in the superconducting phase suggests the possibility of the chiral $p$- or $f$-wave bogolon pairing instabilities rather than the Pomeranchuk instability. These chiral states coexist with the chiral $d$-wave superconducting state, spontaneously break inversion symmetry, and lead to the disappearance of the torus-shaped BFS structure.