Magnetic Order in 3D Topological Insulators -- Wishful Thinking or Gateway to Emergent Quantum Effects?.

Three-dimensional topological insulators (TIs) are a perfectly tuned quantum-mechanical machinery in which counter-propagating and oppositely spin-polarized conduction channels balance each other on the surface of the material. This topological surface state crosses the bandgap of the TI, and lives at the interface between the topological and a trivial material, such as vacuum. Despite its balanced perfection, it is rather useless for any practical applications. Instead, it takes the breaking of time-reversal symmetry (TRS), and the appearance of an exchange gap to unlock hidden quantum states. The quantum anomalous Hall effect, which has first been observed in Cr-doped (Sb,Bi)$_2$Te$_3$, is an example of such a state in which two edge channels are formed at zero field, crossing the magnetic exchange gap. The breaking of TRS can be achieved by magnetic doping of the TI with transition metal or rare earth ions, modulation doping to keep the electronically active channel impurity free, or by proximity coupling to a magnetically ordered layer or substrate, in heterostructures or superlattices. We review the challenges these approaches are facing in the famous 3D TI (Sb,Bi)$_2$(Se,Te)$_3$ family, and try to answer the question whether these materials can live up to the hype surrounding them.