Quantum mold casting for topological insulating and edge states

We study the possibility of transferring fermions from a trivial system as particle source to an empty system but at topological phase as a mold for casting a stable topological insulator dynamically. We show that this can be realized by a non-Hermitian unidirectional hopping, which connects a central system at topological phase and a trivial flat-band system with a periodic driving chemical potential, which scans over the valence band of the central system. The near exceptional-point dynamics allows a unidirectional dynamical process: the time evolution from an initial state with full-filled source system to a stable topological insulating state approximately. The result is demonstrated numerically by a source-assistant QWZ model and SSH chain in the presence of random perturbation. Our finding reveals a classical analogy of quench dynamics in quantum matter and provides a way for topological quantum state engineering.