We consider the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state with an angle dependent-gap (ADG) for the arbitrary angle theta_0 between the direction of the Cooper pair momentum and the symmetry axis of the ADG in asymmetric nuclear matter. We find t
wo kinds of locally stable states, i.e., the FFLO-ADG-orthogonal and FFLO-ADG-parallel states, which correspond to theta_0=pi/2 and theta_0=0, respectively. Furthermore, the-FFLO-ADG-orthogonal state is located at small asymmetry, whereas the FFLO-ADG-parallel state is favored for large asymmetry. The critical isospin asymmetry alpha_c, where the superfluid vanishes, is enhanced largely by considering the Cooper pair momentum with an ADG.
We propose an axisymmetric angle-dependent gap (ADG) state with the broken rotational symmetry in isospin-asymmetric nuclear matter. In this state, the deformed Fermi spheres of neutrons and protons increase the pairing probabilities along the axis o
f symmetry breaking near the average Fermi surface. We find that the state possesses lower free energy and larger gap value than the angle-averaged gap state at large isospin asymmetries. These properties are mainly caused by the coupling of different m_{j} components of the pairing gap. Furthermore, we find the transition from the ADG state to the normal state is of second order and the ADG state vanishes at the critical isospin asymmetry m_{j} where the angle-averaged gap vanishes.
