Modeling potentiometric measurements in topological insulators including parallel channels

Abstract

The discovery of spin-polarized states at the surface of three-dimensional topological insulators (TI) like Bi${}_{2}$Te${}_{3}$ and Bi${}_{2}$Se${}_{3}$ motivates intense interests in possible electrical measurements demonstrating unique signatures of these unusual states. Here we show that a three-terminal potentiometric set-up can be used to probe them by measuring the voltage change of a detecting magnet upon reversing its magnetization. We present numerical results using a nonequilibrium Green's function (NEGF)-based model to show the corresponding signal quantitatively in various transport regimes. We then provide an analytical expression for the resistance (the measured voltage difference divided by an applied current) that agrees with NEGF results well in both ballistic and diffusive limits. This expression is applicable to TI surface states, two-dimensional electrons with Rashba spin-split bands, and any combination of multiple channels, including bulk parallel states in TI, which makes it useful in analyzing experimental results.