ABSTRACT
The quantum Hall effect (QHE) is example of dissipationless electrical transport that can occur when a large magnetic field is applied to a high mobility two-dimensional electron gas at absolute zero. As QHE depends on a large applied magnetic field, it was natural to ask if a material could possess similar quantized transport inherently, without Landau levels from external fields. The surface states under the magnetic domains can be gapped by exchange coupling, and acquire a mass, whose sign is dependent on the direction of magnetization of the overlying domain. One way to accomplish this is to make the TI itself ferromagnetic by magnetic doping, and to control the carrier density so that chemical potential lies inside the magnetic gap. The choice of magnetic dopant is thus crucial for the realization of the quantum anomalous Hall effect. Ferromagnetism arises in dilute magnetic semiconductors via the carrier-mediated Ruderman–Kittel–Kasuya–Yosida exchange interaction.
