Scanning tunneling spectroscopy study of quasiparticle interference on the dual topological insulator ${\mathrm{Bi}}_{1-x}{\mathrm{Sb}}_x$

Electronic states of the topological insulator ${\mathrm{Bi}}_{1-x}{\mathrm{Sb}}_x$, which is nontrivial in terms of both the $Z_2$ index and the mirror Chern number, were studied by quasiparticle interference (QPI) using low-temperature scanning tunneling spectroscopy. Our Fourier-transform analysis of the QPI patterns reveals the dispersion of the two surface bands above the Fermi energy ($E_F$). Absence of the surface band crossing is unambiguously confirmed, which allowed us to elucidate the mirror Chern number of this system is $-1$. We also found that Co atoms deposited onto a clean surface of ${\mathrm{Bi}}_{1-x}{\mathrm{Sb}}_x$ create impurity states with a clover-leaf-like shape at around 80 meV above $E_F$. While additional spin-flipping scatterings due to those Co atoms cannot be detected by QPI because of the inherent absence of interference between states with antiparallel spins, we observed clear enhancement of spin-conserving scatterings after Co deposition.

Figure 1

(a) STM image of a 93 nm $\times$ 93 nm region on a clean surface of ${\mathrm{Bi}}_{1-x}{\mathrm{Sb}}_x$ obtained at a constant current mode. (Setpoint: 200 pA at 500 mV.) The inset shows the close up image of a 5 nm $\times$ 5 nm region revealing the hexagonal lattice of surface atoms. (Setpoint: 500 pA at 500 mV.) (b) Average of $256\times 256$ tunneling spectra measured on the same region. The peaks at $E_1$, $E_2$, and $E_3$ are the van Hove singularities related to the surface bands. (Bias modulation: 7 ${\mathrm{mV}}_{\mathrm{rms}}$ at 396 Hz; setpoint: 500 pA at 500 mV.) (c) Spatial mapping of $dI/dV$ at $+80$ mV of the same region. (d) FT image calculated from the $dI/dV$ in (c). All the equivalent points are averaged to increase signal-to-noise ratio. The hexagon represents the size and the orientation of the surface Brillouin zone. The dashed square represents the area displayed in the FT images in Figs. 2–2.

Figure 2

(a)–(d) FT of $dI/dV$ maps at $E=-140,-40,+160$, and $+260$ meV on a clean surface of ${\mathrm{Bi}}_{1-x}{\mathrm{Sb}}_x$. (e) Profiles of the FT images in the $\overline{\Gamma }\text{−}\overline{M}$ and the $\overline{\Gamma }\text{−}\overline{K}$ directions plotted in grayscale. The arrow at around $-100$ meV in the $\overline{\Gamma }\text{−}\overline{M}$ direction indicate an artifact which disappears in the FT of $(dI/dV)/(I/V)$ maps [21]. (f) Profiles along the dotted straight line in (c). This shows the dispersion along the $\overline{\Gamma }\text{−}\overline{K}$ of the feature enclosed by dotted ellipses in (c). (g) Peak positions of the FT profiles. The size (area) of each marker is proportional to the peak intensity. The dashed line around 70 meV is a possible FT peak corresponding to QPI within the B pocket, but not analyzed in detail. (h) Peak positions of the profile in (f). (i)–(l) Schematic CCE in the four energy ranges: (i) $E<E_1$, (j) $E_1<E<E_2$, (k) $E_2<E<E_3$, and (l) $E_3<E$. The pockets are labeled by A–E. The scattering vectors corresponding to the observed FT peaks are labeled by ${\mathbf{q}}_1\text{−}{\mathbf{q}}_{11}$. ${\mathbf{q}}_5^{\prime }$ in the profile image in (h) denotes the $\overline{\Gamma }\text{−}\overline{K}$ component of the wave vector ${\mathbf{q}}_5$. Dotted curves in (d) indicate the tails of the spot labeled by ${\mathbf{q}}_{11}$, and ${\mathbf{q}}_{10}$ corresponds to the intersection of the two tails.

Figure 3

(a) Surface band structure of the clean surface of ${\mathrm{Bi}}_{1-x}{\mathrm{Sb}}_x$ reconstructed from our QPI data. Previous ARPES data [9] with an energy resolution of 18 meV are also plotted. The dashed curves are a guide to the eye. (b) Surface band structure of the same sample after the deposition of Co. The dashed curves same as those in (a) are drawn.

Figure 4

(a) STM image of a 93 nm $\times$ 93 nm region of ${\mathrm{Bi}}_{1-x}{\mathrm{Sb}}_x$ after depositing a small amount of Co. (Setpoint: 500 pA at 500 mV.) (b) $dI/dV$ map at $+80$ meV of the same region as (a). The inset shows $dI/dV$ map of a 12 nm $\times$ 12 nm on the same surface. (Bias modulation: 7 ${\mathrm{mV}}_{\mathrm{rms}}$ at 396 Hz; setpoint: 500 pA at 500 mV.) (c) Tunneling spectra obtained across one of the clover-leaf-like shaped impurity states. The measurement locations are indicated by the arrow in (c). The thick curve is the spectrum at the center of the clover-leaf-like shape. (d) FT profiles of $dI/dV$ maps after the Co deposition. (e) Position and intensity of FT peaks. The area of each marker is proportional to the peak intensity.