Relocating a topogical state using non-Hermitian defects

Topological midgap states are expected to appear at the interface between structurs with trivial and non-trivial topologies. Here, I show that a single embedded non-Hermitian defect in a one-dimensional topological system at certain degrees of non-Hermiticity can remove the topological mode from the edge and restore it inside the lattice at the same place where the non-Hermitian defect is placed. I relate this unexpected phenomenon to the wave-matching condition and continuity of the wave function at different sites in the lattice. These findings pave the way for controlling the position of topological states at will.