Wave-Packet Dynamics in Quantum Spin Hall Systems

In the context of research on topological phases of matter, quantum spin Hall (QSH) systems are especially interesting for applications in spintronics. In this work, we study numerically the dynamics of wave packets in mercury telluride (HgTe) quantum wells. This system presents topologically-protected spin polarized edge states (a signature of the QSH effect) when the width of the well is larger than a critical value (d > d_c ~ 6.3 nm). In our simulations, we consider the evolution of Gaussian wave-packet using the BHZ Hamiltonian through the (Fourier) split-operator method. We observe the oscillatory behavior of the mean position of the packet, closely related to the effect of zitterbewegung. We also study the spin separation of the package into edge-state-like patterns. The strong dependence of this behavior with the initial conditions and the presence of electrical fields (in-plane) are also discussed.