Spontaneous topological pumping in non-Hermitian systems

We introduce modulational instability in non-Hermitian systems to study state conversion of topological edge states. We show that state conversion in non-Hermitian systems leads to topological pumping, which is a way of transferring topological edge state from one edge to the opposite edge. In contrast to Hermitian systems, topological pumping can occur spontaneously in non-Hermitian systems.