  The counterpropagating edge states of a two-dimensional topological insulator
(TI) carry electrons of opposite spins. We investigate the transport properties
of edge states in a two-dimensional TI which is contacted to ferromagnetic
leads. The application of a side-gate voltage induces a constriction or quantum
point contact (QPC) which couples the two edge channels. The transport
properties of the system is calculated via the Keldysh nonequilibrium Green's
function method. We found that inter-edge spin-flip coupling can significantly
enhance (suppress) the charge current when the magnetization of the leads are
anti-parallel (parallel) to one another. On the other hand, spin-conserving
inter-edge coupling generally reduces the current by backscattering regardless
of the magnetization configuration. The charge current and the conductance as a
function of the bias voltage, also exhibit similar trends with respect to
spin-flip coupling strength, for both parallel and anti-parallel
configurations. Hence, gate voltage modulation of edge states via a QPC can
provide a means of modulating the spin or charge current flow in TI-based
spintronics devices.
