  Inverted HgTe/CdTe quantum wells have been used as a platform for the
realization of 2D topological insulators, bulk insulator materials with
spin-helical metallic edges states protected by time-reversal symmetry. This
work investigates the spectrum and the charge transport in HgTe/CdTe quantum
well junctions both in the topological regime and in the absence of
time-reversal symmetry. We model the system using the BHZ effective Hamiltonian
and compute the transport properties using recursive Green's functions with a
finite differences' method. Specifically, we have studied the material's
spatially-resolved conductance in a set-up with a gated central region, forming
monopolar (n-n$^{\prime}$-n) and heteropolar (n-p-n, n-TI-n) double junctions,
which have been recently realized in experiments. We find regimes in which the
edge states carry spin-polarized currents in the central region even in the
presence of a small magnetic field, which breaks TRS. More interestingly, the
conductance displays spin-dependent, Fabry-Per\'ot-like oscillations as a
function of the central gate voltage producing tunable, fully spin-polarized
currents through the device.
