Defect solitons in defective PT potentials with real part of dual-frequency lattices

We address the properties of defect solitons (DSs) in defective parity-time potentials with real part of dual-frequency lattices. The impact of defect on stability regions of DSs was considered. For positive defects, DSs whose real/imaginary parts are symmetric/antisymmetric (SA) functions of position are always stable in the semi-infinite gap and nonexistent in the first gap. While for negative defects, in semi-infinite gap, the SADSs are stable in most of their existence region besides low power region, but in the first gap, all the SADSs are stable. The ASDSs are unstable in the whole semi-infinite gap regardless of defects, but can be stable in the low power region for positive defects.