Figure 1: (a) Illustration of the conventional integer quantum Hall effect found, e.g., in 2D semiconductor systems. (b) Illustration of the unconventional half-integer quantum Hall effect found, e.g., in a graphene layer. (c) The experimentally observed Landau quantization of the topological surface states in ${\text{Bi}}_2{\text{Se}}_3$ for several magnetic field strengths. Curves are offset vertically for clarity. Note in particular the peak occurring at the Fermi level (around $-200\text{mV}$ sample bias), which is independent of the field strength. This serves as a hallmark of the unconventional quantization form shown in (b). (d) STM picture of a ${\text{Bi}}_2{\text{Se}}_3$ surface in the presence of triangular-shaped defects (bright white spots). By selecting one point in such a map and plotting the $dI/dV$ curves as a function of bias voltage, one is able to probe the density of states similarly to (c).