The typical bulk model describing 2D topological insulators (TI) consists of two types of spin-orbit terms, the so-called Dirac term which induces out-of plane spin polarization and the Rashba term which induces in-plane spin polarization. We show th
at for some parameters of the Fermi energy, the beam splitter device built on 2D TIs can achieve higher in-plane spin polarization than one built on materials described by the Rashba model itself. Further, due to high tunability of the electron density and the asymmetry of the quantum well, spin polarization in different directions can be obtained. While in the normal (topologically trivial) regime the in-plane spin polarization would dominate, in the inverted regime the out-of-plane polarization is more significant not only in the band gap but also for small Fermi energies above the gap. Further, we suggest a double beam splitter scheme, to measure in-plane spin current all electrically. Although we consider here as an example HgTe/CdTe quantum wells, this scheme could be also promising for InAs/GaSb QWs where the in- and out-of-plane polarization could be achieved in a single device.
We analyze thermally induced spin and charge transport in HgTe/CdTe quantum wells on the basis of the numerical non-equilibrium Greens function technique in the linear response regime. In the topologically non-trivial regime, we find a clear signatur
e of the gap of the edge states due to their finite overlap from opposite sample boundaries -- both in the charge Seebeck and spin Nernst signal. We are able to fully understand the physical origin of the thermoelectric transport signatures of edge and bulk states based on simple analytical models. Interestingly, we derive that the spin Nernst signal is related to the spin Hall conductance by a Mott-like relation which is exact to all orders in the temperature difference between the warm and the cold reservoir.
