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Quantum anomalous Hall effect has been predicted in HgMnTe quantum wells withan out-of-plane magnetization of Mn atoms. However, since HgMnTe quantum wellsare paramagnetic, an out-of-plane magnetic field is required to polarizemagnetic moments of Mn atoms, which inevitably induces Landau levels and makesit difficult to identify the origin of the quantized Hall conductanceexperimentally. In this work, we study the quantum anomalous Hall effect in thepresence of an in-plane magnetic field in Mn doped HgTe quantum wells. For asmall out-of-plane magnetic field, the in-plane magnetic field can drive thesystem from a normal insulating state to a quantum anomalous Hall state. Whenthe out-of-plane magnetic field is slightly above the transition point, thesystem shows a reentrant behavior of Hall conductance, varying from $-e^2/h$ to0 and back to $-e^2/h$, with increasing in-plane magnetic fields. The reentrantquantum anomalous Hall effect originates from the interplay between theexchange coupling of magnetic moments and the direct Zeeman coupling ofmagnetic fields. The calculation incorporating Landau levels shows that thereis no qualitative change of the reentrant behavior.

Reentrant quantum anomalous Hall effect with in-plane magnetic fields in HgMnTe quantum wells