Defect solitons in parity-time periodic potentials

In this article, properties of solitons in a parity-time periodical lattices with a single-sited defect are investigated. Both of the negative and positive defects are considered. Linear stability analyses show that, when the defect is positive, in the semi-infinite gap, the solitons are always stable, while in the first gap, the solitons are unstable in most of their existence region except for those near the edge of the second band; when the defect is negative, in the semi-infinite gap, other than those near the edge of the first band, most solitons are stable, but in the first gap, all solitons are unstable. Such stability analyses are corroborated by numerical simulations.