Spin-orbit-coupled spinor gap solitons in Bose-Einstein condensates

Spin-1 spin-orbit-coupled spinor Bose-Einstein condensates have been realized in experiment. We study spin-orbit-coupled spinor gap solitons in this experimentally realizable system with an optical lattice. The spin-dependent parity symmetry of the spin-orbit coupling plays an important role in the properties of gap solitons. Two families of solitons with opposite spin-dependent parity are found. Using an approximate model by replacing the optical lattice with a harmonic trap, we demonstrate the physical origin of the two families. For the zero effective quadratic Zeeman shift, we also find a type of gap soliton that spontaneously breaks the spin-dependent parity symmetry.