  A non-Hermitian topological insulator is fundamentally different from
conventional topological insulators. The non-Hermitian skin effect arises in a
nonreciprocal tight binding lattice with open edges. In this case, not only
topological states but also bulk states are localized around the edges of the
nonreciprocal system. We discuss that controllable switching from topological
edge states into topological extended states in a chiral symmetric
non-Hermitian system is possible. We show that the skin depth decreases with
non-reciprocity for bulk states but increases with it for topological zero
energy states.
