Illustration: Alan Stonebraker

Figure 2: Magneto-optical effect in a 3D topological insulator (TI). (Top) Applying a weak magnetic field to the surfaces of a 3D topological insulator (blue slab) causes an energy gap to open in the spectrum of electronic surface states (grey). This amounts to a half-integer Hall conductivity ($σxy$) on each of its surfaces. (Bottom) The rotation of light that is reflected from (Kerr effect) or transmitted through (Faraday effect) a 3D topological insulator in a magnetic field is given by $arctan(1/α)$ and $arctan(α)$, respectively. These angles are independent of material details. $Eo$, $ER$, and $ET$ represent incident, reflected, and transmitted beams. $θF$ and $θK$ are the Faraday and Kerr angles, respectively.