Wave-packet transport in HgTe

Recent experiments have shown the Quantum Spin Hall State in mercury telluride quantum wells and the associated edge channel transport at zero external magnetic field. We employ a four band model to investigate the propagation of such topological edge state wave-packets in the gap, as well as bulk states in the conducting region. Our recently developed algorithm is able to solve the time-dependent scattering problem for arbitrary scattering potentials and gives revealing insight into the occurring edge phenomena. The obtained time evolution of the wavefunction is used to calculate the complete energy dependent scattering matrix for a time-independent Hamiltonian. With this we investigate the transport in different mesoscopic setups and are particularly interested in the scattering of edge states at constrictions.