Figure 1

Measurement principle of the spin-dependent potential with STM tips. (a) Typical transport measurement setup as seen by the optical microscope. With the four linearly arranged STM tips in contact to the sample surface acting as electrical probes, a current is induced between the outer two tips, while the resulting potential difference is measured between the inner ones. (b) Due to the helical nature of the TSS, the orientation of charge carrier spin is perpendicular to their corresponding momentum \(\hslash \overrightarrow{k}\) and the surface normal, with the intrinsic TSS spin polarisation p being the degree of helicity. The electrical contact between a voltage probe and the TI surface can be regarded as two parallel channels with conductances G_↑ and G_↓ for the two spin orientations. For a finite probe magnetisation (G_↑ ≠ G_↓), the voltage probe acquires a spin-dependent potential V_s, which is given by the interface condition requiring zero current flow (cf. Eq. 1). In this sketch, charge transport takes place in k_x-direction and Δk_x denotes the shift of the Fermi circle due to applied bias. Note that the indicated shift in electrochemical potential \(\hslash {v}_{{\rm{F}}}\Delta {k}_{x}\cos \phi \) refers to the extremal position ϕ = 0.