  Existence and stability of PT-symmetric gap solitons in a periodic structure
with defocusing nonlocal nonlinearity are studied both theoretically and
numerically. We find that, for any degree of nonlocality, gap solitons are
always unstable in the presence of an imaginary potential. The instability
manifests itself as a lateral drift of solitons due to an unbalanced particle
flux. We also demonstrate that the perturbation growth rate is proportional to
the amount of gain (loss), thus predicting the observability of stable gap
solitons for small imaginary potentials.
