Suspended Nanowires as Mechanically Controlled Rashba Spin Splitters

Suspended nanowires are shown to provide mechanically controlled coherent mixing or splitting of the spin states of transmitted electrons, caused by the Rashba spin-orbit interaction. The sensitivity of the latter to mechanical bending makes the wire a tunable nanoelectromechanical weak link between reservoirs. When the reservoirs are populated with misbalanced “spin-up and spin-down” electrons, the wire becomes a source of split spin currents, which are not associated with electric charge transfer and which do not depend on temperature or driving voltages. The mechanical vibrations of the bended wires allow for additional tunability of these splitters by applying a magnetic field and varying the temperature. Clean metallic carbon nanotubes of a few microns length are good candidates for generating spin conductance of the same order as the charge conductance (divided by $e^2$) which would have been induced by electric driving voltages.

Figure 1

A break junction supporting a nanowire of length $d$ (possibly a carbon nanotube), attached by tunnel contacts to two biased electrodes ([$L$] and [$R$]). The small vibrations of the wire induce oscillations in the angle $\theta$ around some value ${\theta }_0$. The upper electrode ([$G$]) is an STM tip biased differently. The Rashba interaction can be controlled via the bending angle $\theta$ of the wire. The latter can be modified both mechanically, by loads (shown by the arrows) applied to the substrate and electrically, by biasing the STM.

Figure 2

Schematic geometry used for calculating the spin-orbit coupling dependence of the tunneling amplitude. A localized level is tunnel coupled to left ($L$) and right ($R$) electronic electrodes with possibly different chemical potentials ${\mu }_{L\sigma }$ and ${\mu }_{R\sigma }$. The setup lies in the $x\mathrm{\text{−}}y$ plane; a magnetic field applied along $\widehat{\mathbf{z}}$ is shown by $\otimes$. The setup corresponds to a configuration in which the wire is controlled only mechanically, and the STM is not shown.