Multi-terminal potentiometric spin signal measurement on channels with spin-momentum locking

We will discuss multi-terminal potentiometric measurements on channels with spin-momentum locking (SML) e.g. topological insulator, Rashba interface, heavy metals etc. Using these results in conjunction with the Onsager reciprocity relation [1], we argue that multi-terminal spin valves on such channels [2] should show two distinct values of anti-parallel resistance $R_{AP}^{(1)}$ and $R_{AP}^{(2)}$ such that $R_{AP}^{(1)}>R_P>R_{AP}^{(2)}$ depending on the direction of spin flow relative to SML ($R_P$: parallel resistance). This remarkable signature originating from SML can only be observed in multi-terminal measurements and has been experimentally observed recently on heavy metals [3]. We argue from Onsager reciprocity that 2-terminal measurement will only show the usual result $R_{AP}^{(1)}=R_{AP}^{(2)}>R_P$. We present numerical results using a detailed semiclassical model which uses four electrochemical potentials depending on group velocity ($+$ or $-$) and spin polarization (up or down) of the channel electronic states. Finally, we propose novel spintronic applications based on the potentiometric measurement. [1] Jacquod et al., Phys. Rev. B 86, 155118, 2012. [2] Sayed et al., Sci. Rep. 6, 35658, 2016. [3] Pham et al., Nano Lett., DOI:10.1021/acs.nanolett.6b02334, 2016.