Invisibility in non-Hermitian tight-binding lattices

Reflectionless defects in Hermitian tight-binding lattices, synthesized by the intertwining operator technique of supersymmetric quantum mechanics, are generally not invisible and time-of-flight measurements could reveal the existence of the defects. Here it is shown that, in a certain class of non-Hermitian tight-binding lattices with complex hopping amplitudes, defects in the lattice can appear fully invisible to an outside observer. The synthesized non-Hermitian lattices with invisible defects possess a real-valued energy spectrum, however they lack of parity-time (PT) symmetry, which does not play any role in the present work.