Implementation of a unitary algorithm in the analysis of quantum dynamics at the interface between a topological insulator and a conductor

At the interface between a conductor and a topological insulator, it is expected that the hybridization between quantum modes leads to a non-trivial spin-dynamics of a quantum state, because a helical boundary mode is quite spin-selective. It is also interesting to explore the condition for the efficient injection of a quantum state into the helical edge channels, which would show a spin-filter effect. In order to explore this situation, we construct a model for the interface and make an attempt to implement a stable and unitary algorithm in the numerical analysis of quantum wave-packet dynamics.