Quantum Anomalous Hall Effect in Hg${}_{1-y}$Mn${}_y$Te Quantum Wells

The quantum Hall effect is usually observed when the two-dimensional electron gas is subjected to an external magnetic field, so that their quantum states form Landau levels. In this work we predict that a new phenomenon, the quantum anomalous Hall effect, can be realized in Hg${}_{1-y}$Mn${}_y$Te quantum wells, without the external magnetic field and the associated Landau levels. This effect arises purely from the spin polarization of the $Mn$ atoms, and the quantized Hall conductance is predicted for a range of quantum well thickness and the concentration of the $Mn$ atoms. This effect enables dissipationless charge current in spintronics devices.