Theory of spin-Hall effect in HgTe

We study theoretically a ballistic transport in HgTe H-shaped nanostructures using Landauer-Buettiker formalism. We model inverted HgTe nanostructures using realistic parameters describing properly the spin-orbit splittings and effective mass in these structures. The idea of the transport measurements is as follows. When an electric current flows in one of the legs of the H-bar structure, a transverse spin current due to the intrinsic spin-Hall effect is induced in the connecting part. Subsequently, this spin current produces, due to the inverse spin-Hall effect, a voltage difference in the opposite leg of the H-bar structure which can be measured by a voltmeter. We predict that the spin-Hall effect in H-shaped HgTe/HgCdTe inverted band structure quantum wells can be significant (on the order of a few % of the excitation voltage (microvolts)) if the size of the structure is below a ballistic length.