Quantum anomalous Hall effect (QAHE),

The axion insulator which may exhibit an exotic quantized magnetoelectric effect is one of the most interesting quantum phases predicted for the three-dimensional topological insulator (TI). The axion insulator state is expected to show up in magnetically doped TIs with magnetizations pointing inwards and outwards from the respective surfaces. Towards the realization of the axion insulator, we here engineered a TI heterostructure in which magnetic ions (Cr) are modulation-doped only in the vicinity of the top and bottom surfaces of the TI ((Bi,Sb)Te) film. A separation layer between the two magnetic layers weakens interlayer coupling between them, enabling the magnetization reversal of individual layers. We demonstrate the realization of the axion insulator by observing a zero Hall plateau (ZHP) (where both the Hall and longitudinal conductivity become zero) in the electric transport properties, excluding the other possible origins for the ZHP. The manifestation of the axion insulator can lead to a new stage of research on novel magnetoelectric responses in topological matter.

Gigantic magnetoresistance is shown in a Cr- and V-doped topological insulator multilayer, assuring robust axion insulator.

Electronic ordering in magnetic and dielectric materials forms domains with different signs of order parameters. The control of configuration and motion of the domain walls (DWs) enables nonvolatile responses against minute external fields. Here, we realize chiral edge states (CESs) on the magnetic DWs of a magnetic topological insulator. We design and fabricate the magnetic domains in the quantum anomalous Hall state with the tip of a magnetic force microscope and prove the existence of the chiral one-dimensional edge conduction along the prescribed DWs through transport measurements. The proof-of-concept devices based on reconfigurable CESs and Landauer-Büttiker formalism are realized for multiple-domain configurations with well-defined DW channels. Our results may lead to the realization of low-power-consumption spintronic devices.

Electrodynamic responses from three-dimensional topological insulators are characterized by the universal magnetoelectric term constituent of the Lagrangian formalism. The quantized magnetoelectric coupling, which is generally referred to as topological magnetoelectric effect, has been predicted to induce exotic phenomena including the universal low-energy magneto-optical effects. Here we report the experimental indication of the topological magnetoelectric effect, which is exemplified by magneto-optical Faraday and Kerr rotations in the quantum anomalous Hall states of magnetic topological insulator surfaces by terahertz magneto-optics. The universal relation composed of the observed Faraday and Kerr rotation angles but not of any material parameters (for example, dielectric constant and magnetic susceptibility) well exhibits the trajectory towards the fine structure constant in the quantized limit.