Quantum Anomalous Hall Effect in Magnetically Doped InAs/GaSb Quantum Wells

The quantum anomalous Hall effect has recently been observed experimentally in thin films of Cr doped (Bi,Sb)$_2$Te$_3$ at low temperature ($\sim$ 30mK). In this work, we propose realizing the quantum anomalous Hall effect in more conventional diluted magnetic semiconductors with magnetically doped InAs/GaSb type II quantum wells. Based on a four band model, we find a large increase of the Curie temperature for ferromagnetism due to the band edge singularity in the inverted regime of InAs/GaSb quantum wells. Below the Curie temperature, the quantum anomalous Hall effect is confirmed by the direct calculation of Hall conductance. Remarkably, our calculation based on eight-band Kane model reveals a band gap induced by exchange coupling reaching 10meV. The high sample quality and strong exchange coupling make the magnetically doped InAs/GaSb quantum well a good candidate for the quantum anomalous Hall insulator at high temperature.