Currents of topological marker in dynamically controlled Chern Insulators

Motivated by the recent development of the local Chern marker theory we propose a new perspective on the dynamics of the topological markers. This approach allows us to introduce the currents of the marker explicitly. Our definition satisfies the lattice continuity equation and has a clear physical interpretation in terms of density currents. Using this method, we demonstrated numerically the position control of a topologically nontrivial subsystem inside a finite sample. We believe that our framework will help to understand the dynamics of inhomogeneous topological insulators.