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 the topological edge state from one edge to the opposite edge. In contrast to Hermitian systems, topological pumping can occur spontaneously in non-Hermitian systems. We show that topological edge state transfer occurs fast.

Figure 1

The (normalized) density plots as functions of $n$ and time at $\gamma =0.2$ for topological left and right edge states in (a,b) and for bulk states with eigenvalues $E=1.97+i\gamma$ and $1.53+i\gamma$ in (c) and (d), respectively. We initially add very small amplitude modulation to these states. The topological right edge state is the only modulationally stable state in the system. It is interesting to see that the topological left edge state is transported to the other edge, and all the bulk states evolve to the topological state at the right edge. The state conversion occurs at around $t=20$, which decreases rapidly with increasing $E_I$. In (c,d), we plot the figures up to $t=400$ to confirm that no other state conversion occurs.