Defect matter-wave gap solitons in spin–orbit-coupled Bose–Einstein condensates in Zeeman lattices

• For repulsive defect, fundamental solitons are stable in the semi-infinite, first, and second gaps in SOC-BECs in Zeeman lattices.
• For repulsive defect, gap-stripe solitons can be stable in the semi-infinite and first gaps in SOC-BECs in Zeeman lattices.
• For attractive defect, fundamental solitons only stably exist in the semi-infinite gap.

We report on the properties of fundamental defect matter-wave gap solitons in spin–orbit-coupled Bose–Einstein condensates in one-dimensional Zeeman lattices with attractive nonlinearity. One component of these solitons is a real even function, and the other is an imaginary odd function. When the defect is repulsive, these solitons can be stable in the semi-infinite, first, and second gaps. Increasing the strength of spin–orbit coupling, stable defect gap-stripe solitons in the semi-infinite and first gaps are found. However, for an attractive defect, the solitons only stably exist in the semi-infinite gap and cannot be close to the lower edge of the first Bloch band.