Single crystal of Bi₂Te₂Se was grown by the self-flux method following the previously reported procedure (Ren et al., 2010). Bulk-insulating property of the Bi₂Te₂Se was confirmed by ex situ transport measurement with physical property measurements system (PPMS), which displayed increasing bulk resistivity with decreasing temperature (Ko et al., 2018). In situ transport and STP measurements were done at the cryogenic four-probe STM, operating at ultrahigh vacuum (< 8 × 10^–10 Torr) and temperature of 82 K (Kim et al., 2007). The samples were cleaved inside the ultrahigh-vacuum chamber and then transferred to the STM stage without any exposure to the ambient environment. Etched tungsten tips were used as STM probes, whose metallic behavior was checked on gold foil before each measurement. The samples are confirmed to be thicker than 500 μm after cleaving which ensures no crosstalk between the top and bottom surface states or leakage current to the sample holder.

VPTS spectroscopy was acquired by performing four-probe transport measurements in collinear configuration while changing the position of two inner voltage probes (Durand et al., 2016; Hus et al., 2017; Ko et al., 2018). Figure 1A illustrates the measurement scheme over the surface with atomic steps. Here, two outer probes supply the source current while two inner probes measure the potential difference. The potential drop between the inner probes is measured for a large set of inter-probe distances measured by scanning electron microscope (SEM). In topological insulators, transport occurs through two conduction channels of the topological surface states and the trivial bulk states. Assuming uniform and isotropic 2D and 3D resistivity for surface and bulk, respectively, the four-probe resistance can be expressed as a function of probe spacings (Durand et al., 2016) as R = Δ V I s = ρ 2 D ⋅ 1 2 π ln [ ( g + s 14 s 12 ) ( g + s 14 s 34 )   ( g + s 14 s 13 ) ( g + s 14 s 24 ) ] = ρ 2 D ⋅ Χ g where ΔV is the potential drop between the inner voltage probes, I _s is the source current applied through the outer current probes, ρ _2D is the surface resistivity, s _ij is the distance between the probes i and j, and g = (ρ _2D/ρ _3D)s ₁₄ is a dimensionless parameter which gives the ratio of the surface and bulk resistivity. The model indicates that R vs. X _g should be linear when the correct value of g is substituted.

STP is a unique technique that combines transport with the scanning capability of STM (Clark et al., 2013; Li et al., 2013; Clark et al., 2014). The measurement schematic of STP is shown in Figure 1B. Here, two outer probes supply the source current while an inner probe scans the surface. To measure the potentiometry, we adopted the modified version of Feenstra and co-worker’s approach (Feenstra et al., 1986; Fein et al., 1987; Lüpke et al., 2015), where the scanning probe first moved to the new point and measured the surface topography at finite DC bias voltage by traditional STM feedback based on tunneling current, and then the STM feedback was turned off and a second feedback loop on the tip bias was turned on to track the surface potential by regulating tunneling current to zero. The resulting height and potential profile visualize the topography and potential of the scanned region.

VPTS was applied to Bi₂Te₂Se to observe the effect of atomic steps on the transport through the topological surface states. To exclude the effect of bulk conduction, the surface dominant transport was achieved by lowering the measurement temperature to 82 K and reducing the source probe distance below 10 μm (Ko et al., 2018). Figure 2A shows the SEM image of the surface of Bi₂Te₂Se that does not display any distinguishable steps, and Figure 2C shows the results of VPTS taken on this pristine surface with source probe distance s ₁₄ = 5.1 μm. The best linear fitting between R and X _g was achieved when g = 0, indicating that 100% of the electrical current is carried by the surface states. The linear fit results in the zero offset at X _g = 0 and the coefficient of determination r ² = 0.9981, showing that the measured four-probe resistances follow the theoretical prediction of homogenous surface resistivity. From the slope, surface resistivity is estimated to be ρ _2D = 1835 ± 72 Ω. On the other hand, when there are two or more atomic steps between the probes (Figure 2B), measured resistance values become visibly deviated from the homogenous surface resistivity model (Figure 2D, also see Supplementary Figure S1), indicated by lower r ² = 0.9843 and nonzero offset at X _g = 0. Nevertheless, the best linear fit of R vs. X _g was achieved when g = 0 and the surface resistivity is estimated to be ρ _2D = 2,211 ± 250 Ω, which is similar to the pristine surface. The value of fitting parameters indicates that the conduction is still dominated by the surface channel. The visible distortion of resistance values further supports the surface dominant transport, because the bulk conduction would not be affected by atomic steps due to their negligible thickness compared to the sample size (>500 μm). The results clearly show that the atomic steps disturb the transport of charge carriers through the topological surface states, even though the steps do not break time-reversal symmetry.

Further quantitative measurement is achieved by measuring the potential profile with STP across the single atomic step. Figure 3A shows the SEM image of a step edge and the probes placed for STP measurement. The distance between the outer probes was set to 7.9 μm to guarantee the surface dominant transport as confirmed by VPTS. Even though the SEM image can only resolve a single step, STM topography shows that there are two adjacent steps with the height of four QL and one QL (Figures 3B,E), where one QL corresponds to the height of ∼1 nm (Ren et al., 2010). Figure 3C shows the potential map obtained around these steps while flowing the current of 100 μA between the outer probes. Along the flat surface, a smooth potential gradient along the current direction (white arrow) is evident together with the sharp potential drops at the step edges. The potential drops at the step edges become clearer when the background slope is subtracted from the potential profile (Figure 3D). To confirm that these sharp potential drops are not artifacts, we measured the potential profiles across the step edge for various source-drain current values (Figure 3F). The profiles show that as the current increases both the overall slope of the potential and the magnitude of sharp drops at the step edges increase. The increase of potential drops at step edges becomes more visible after subtraction of the background slope (Figure 3G). The consistency between the STP map and single scan lines was confirmed by comparing voltage profiles from the line average of the map and the single scan line at the same current (Supplementary Figure S2).

The resistivity of the surface and atomic steps can be extracted from the current dependence of the overall potential slope and potential drops at the steps, respectively. Since the scanned area is located close to the midpoint between the source probes and the scanning size of 500 nm is much smaller than the source probe distance of 7.9 μm, we can assume a constant current density j → across the scanned area and estimate its magnitude as | j → | = 1 2 π | s 12 ^ s 12 + s 23 ^ s 23 | ⋅ I s = 79340 ⋅ I s ( A / m ) where s i j ^ is the unit vector along the s _ij . Figure 4A shows the values of potential slope dV/dx extracted from the potential profiles in Figure 3F. The graph exhibits linear dependence between dV/dx and I _s , and ρ _2D can be extracted from the slope of the graph as ρ 2 D = E j =   d V d x ⋅ 1 cos 55 ° 79340 ⋅ I s = 244   ± 26   Ω where 55° is the angle between the current and scan directions. The value of ρ _2D is smaller than the one from VPTS, probably due to the aging of the surface that was exposed to a residual gas pressure of 2 × 10^–9 torr for 4 days (Durand et al., 2016; Ko et al., 2018).

Figure 4B shows the measured potential drops at the step edges for different source currents. The voltage drops between the adjacent terraces were extracted by taking the average and standard deviation of the voltages inside the single terraces and then subtracted them to get the magnitude and error of the voltage drops (Supplementary Figure S3). Although the linear trend is less obvious due to the small signal-to-noise ratio, the general trend clearly shows an increasing magnitude of potential drop with the current. Linear fits result in the slope of ∆V _s /I _s = 0.421 Ω for one QL step and ∆V _s /I _s = 0.512 Ω for four QL step, which results in the step resistivity of ρ _s = ∆V _s /j = 0.530 mΩ · cm for one QL step and ρ _s = 0.646 mΩ · cm for four QL step. These results show that atomic steps as small as one QL can scatter charge carriers flowing through the topological surface states and behave as a potential barrier. The value of ρ _s is comparable to the previously reported value of ∼ 1 mΩ · cm for the steps on Bi chalcogenide thin films measured by STP (Bauer and Bobisch, 2016; 2017; Lüpke et al., 2017). Also, it is notable that the value of ρ _s is almost identical for one QL and four QL steps, which indicates that step resistivity is almost independent of the step height. Weak dependence of the resistivity on step height is in contrast with other trivial 2D metallic systems (Homoth et al., 2009; Ji et al., 2012; Clark et al., 2013; Clark et al., 2014) and might be related to the topological nature of the surface states. Revealing the origin of such behavior would require further systematic measurement of resistivity over various step heights and detailed theoretical modeling of atomic steps in topological insulators.