Free fermion entanglement with a semitransparent interface: the effect of graybody factors on entanglement islands

We study the entanglement entropy of free fermions in 2d presence a partially transmitting interface that splits Minkowski space into two half-spaces. focus on case single interval straddles defect, and compute its three limits: Perturbing away from fully reflecting cases, perturbing amount asymmetry about defect. Using these results within setup Poincaré patch AdS _2 2 statically coupled to zero temperature flat bath, we calculate effect boundary location island region. The is toy model for black hole graybody factors. Our indicate region behaves monotonic fashion as function transmission/reflection coefficient at interface.