The funneling effect in a non-Hermitian Anderson model

Abstract

The topological funneling effect, i.e., the motion of an arbitrary excitation to a focal point of the lattice no matter where the lattice is excited, is a dynamical effect due to the non-Hermitian skin effect. This effect disappears in the presence of strong disorder where the system is topologically trivial. In Anderson localized regime with complex spectrum, the motion shows jumpy behavior and the focal point can be any point along the lattice as it is not possible to say its exact place in an experiment a priori. We study transport phenomena in a non-Hermitian system, exhibiting both funneling effect and non-Hermitian jumps. We show that the competition between the skin and Anderson localizations may result in the creation of an extended eigenstate. This can lead to disorder-induced dynamical delocalization in topologically nontrivial region.