Charge puddles in the bulk and on the surface of the topological insulator ${\mathrm{BiSbTeSe}}_2$ studied by scanning tunneling microscopy and optical spectroscopy

The topological insulator ${\mathrm{BiSbTeSe}}_2$ corresponds to a compensated semiconductor in which strong Coulomb disorder gives rise to the formation of charge puddles, i.e., local accumulations of charge carriers, both in the bulk and on the surface. Bulk puddles are formed if the fluctuations of the Coulomb potential are as large as half of the band gap. The gapless surface, in contrast, is sensitive to small fluctuations but the potential is strongly suppressed due to the additional screening channel provided by metallic surface carriers. To study the quantitative relationship between the properties of bulk puddles and surface puddles, we performed infrared transmittance measurements as well as scanning tunneling microscopy measurements on the same sample of ${\mathrm{BiSbTeSe}}_2$, which is close to perfect compensation. At 5.5 K, we find surface potential fluctuations occurring on a length scale $r_s=40–50$ nm with amplitude $\mathrm{\Gamma }=8–14$ meV, which is much smaller than in the bulk, where optical measurements detect the formation of bulk puddles. In this nominally undoped compound, the value of $\mathrm{\Gamma }$ is smaller than expected for pure screening by surface carriers, and we argue that this arises most likely from a cooperative effect of bulk screening and surface screening.

Figure 1

(Left) Optical conductivity ${\sigma }_1\left(\omega \right)$ of ${\mathrm{BiSbTeSe}}_2$ in the frequency range above the phonons and below the band gap, showing a broad temperature-dependent low-energy feature, which we attribute to a Drude-like peak. Dashed gray lines depict Drude-Lorentz fits using a Drude peak plus a single Lorentzian for the onset of interband excitations. (Right) Effective carrier density $N_{\mathrm{eff}}$ as obtained from the fits of ${\sigma }_1\left(\omega \right)$. The nonmonotonic behavior of $N_{\mathrm{eff}}\left(T\right)$ directly tracks the nonmonotonic behavior of ${\sigma }_1({\omega }_0,T)$ at, e.g., $\hslash {\omega }_0=100$ meV.

Figure 2

(a) Atomically resolved STM topograph of cleaved ${\mathrm{BiSbTeSe}}_2$ (10 nm $\times$ 10 nm, $V=-300$ mV, $I=50$ pA). The height profile along the blue line is plotted below the STM image. (b) Characteristic STS spectrum at 5.5 K. The main spectral features (bulk valence-band maximum, Dirac point, and bulk conduction-band minimum) are marked by dashed lines and linked to the sketch of the band structure in the inset, which follows the ARPES result for ${\mathrm{BiSbTeSe}}_2$ [27].

Figure 3

(a) 50 STS spectra over an energy range from $-40$ meV below the Fermi level to 80 meV above, taken in equidistant steps along a straight line of 80 nm length. The shift of the Dirac point (lowest $dI/dV$ value) is of the order of 20 meV. (b) Color codes for (a), (c), and (d). (c) STS map recorded at 5.5 K (100 nm $\times$ 60 nm, $V=50$ mV, $I=70$ pA). Fluctuations in the $dI/dV$ signal visualize the fluctuations in the energy of the Dirac point. (d) STS map recorded at 77 K (100 nm $\times$ 60 nm, $V=80$ mV, $I=50$ pA). (e) Distribution of the Dirac point energy at 5.5 K. (f) Same distribution at 77 K (see main text). (g) and (h) show the same data as in (e) and (f), but corrected for possible tip effects (see main text). Gaussian fits to distributions are shown as black lines. The bins in (e) to (h) have a width of 3 meV.