Detection of the Spin-Chemical Potential in Topological Insulators Using Spin-Polarized Four-Probe STM

We demonstrate a new method for the detection of the spin-chemical potential in topological insulators using spin-polarized four-probe scanning tunneling microscopy on in situ cleaved ${\mathrm{Bi}}_2{\mathrm{Te}}_2\mathrm{Se}$ surfaces. Two-dimensional (2D) surface and 3D bulk conductions are separated quantitatively via variable probe-spacing measurements, enabling the isolation of the nonvanishing spin-dependent electrochemical potential from the Ohmic contribution. This component is identified as the spin-chemical potential arising from the 2D charge current through the spin momentum locked topological surface states (TSS). This method provides a direct measurement of spin current generation efficiency and opens a new avenue to access the intrinsic spin transport associated with pristine TSS.

Figure 1

(a) Illustration of Dirac-like dispersion and helical spin texture of TSS in 3D TIs in an electric field along the -$x$ direction. Spin orientations are shown with red arrows. The equilibrium Fermi surface under zero electric field is shown with a gray meshed surface. (b) Conceptual drawing of spin-polarized four-probe STM transport measurements. The current is supplied by the pointlike source and drain probes (1 and 4) and the local electrochemical potential is measured by the probes in the middle (2 and 3). The electrochemical potential measured by a nonmagnetic probe (gray) averages over all spin directions while the potential measured by a ferromagnetic probe (red) is sensitive to a particular spin direction. (c) Illustration of the electrical potential measured by nonmagnetic probes (black line) and ferromagnetic probes with magnetizations parallel and antiparallel to the current induced spin polarization of the TSS. (d) When the current direction is reversed, both the Ohmic and the spin voltages change sign making $V(-I)=-V(I)$.

Figure 2

Measured resistance values $R$ with varying probe spacing plotted as a function of $X_g$ on the surface of ${\mathrm{Bi}}_2{\mathrm{Te}}_2\mathrm{Se}$. The source probe spacings are 10.9 and $6.0\mu \mathrm{m}$ for (a) and (b), respectively. Both voltage probes are NM in (a) but one is FM in (b). A linear fit between $R$ and $X_g$ can only be obtained when $g=0$, implying surface dominant transport.

Figure 3

(a) Spin-averaged four-probe STM transport measurements on the surface of ${\mathrm{Bi}}_2{\mathrm{Te}}_2\mathrm{Se}$ with a NM probe. (b) Spin-polarized four-probe STM transport measurements with a FM probe magnetized up on two different surface areas (red squares and stars), and with a FM probe magnetized down (blue stars) on another surface area, respectively.

Figure 4

(a) Topographic STM image of the (001) surface of fresh ${\mathrm{Bi}}_2{\mathrm{Te}}_2\mathrm{Se}$ surface (scale bar: 5 nm). (b) Differential conductance ($dI/dV$) spectra taken on fresh sample showing a minima at $-28\mathrm{meV}$ (Set point: $-500\mathrm{mV}$, 60 pA). (c) Typical IV curves showing a linear behavior from which the values of $R$ are extracted. (d) $\mathrm{\Delta }{V}_s$ vs $I$ plot with a linear fit of data points (red line) and $\mathrm{\Delta }{V}_s$ values calculated with Eq. (1) (blue line). Inset shows $-\overrightarrow{h}·\widehat{y}$ vs $\mathrm{\Delta }{V}_s$ calculated for different values of Fermi energy (${\mu }_F$) using the Eq. (1) with $P_{\mathrm{FM}}=1$.