"Tunnel junction of helical edge states: Determining and controlling
spin-preserving and spin-flipping tunnel processes"
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Helical edge states are the electronic conducting states emerging at the
boundaries of a 2D topological insulator, which are currently under the
spotlight due to their peculiar properties. These channels are characterized by
a tight connection between the electron group velocity and the spin orientation,
and exhibit a perfect transmission, as recently observed in CdTe/HgTe and
InAs/GaSb quantum wells.  When a constriction is realized in the 2D quantum
well, electron tunneling between helical edge states occurs via two types of
channels allowed by time-reversal symmetry, namely spin-preserving (p) and
spin-flipping (f) tunneling processes. Determining and controlling the effects
of these two channels is crucial to the application of helical edge states in
spintronics. We show that, despite the Hamiltonian terms describing these two
processes do not commute, the scattering matrix entries of the related
4-terminal setup always factorize into products of p-terms  and  f-terms
contributions. Such factorization provides an operative way to determine the
transmission coefficient Tp and Tf related to each of the two processes, via
transconductance measurements. 
Furthermore, these transmission coefficients are also found to be controlled
independently by a suitable combination of  two side gate voltages applied
across the junction. This result holds for an arbitrary profile of the tunneling
amplitudes, including disorder in the tunnel region, enabling us to discuss the
effect of the finite length of the tunnel junction, and the space modulation of
both magnitude and phase of the tunneling amplitudes.
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Reference: 
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P. Sternativo and F. Dolcini, Phys. Rev. B 89, 035415 (2014)