Switching spin and charge between edge states in topological insulator constrictions: a transer matrix approach

We show how the different spin polarized edge states of the two-dimensional topological insulator mercury telluride can be selectively switched within an elongated constriction. To this end, we derive an effective onedimensional Hamiltonian incorporating the confinement induced gap between right- and left-moving edge states, as well as an energy dependent effective spin-orbit interaction. By means of a transfer matrix approach, we study the transport properties based on this model Hamiltonian and reveal switching characteristics that can serve as the building block for a three state spin- and charge transistor based on a locally gated topological insulator constriction.

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