Charge puddles in the bulk and on the surface of the topological insulator BiSbTeSe$_2$ studied by scanning tunneling microscopy and optical spectroscopy
The topological insulator 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 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 $Γ= 8-14$ 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 $Γ$ 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.