Parity anomaly driven topological transitions in magnetic field
  Recent developments in solid state physics give a prospect to observe the parity anomaly in (2+1)D massive Dirac systems. Here we show, that the quantum anomalous Hall (QAH) state in orbital magnetic fields originates from the Dirac mass term and induces an anomalous four-current related to the parity anomaly. This differentiates the QAH from the quantum Hall (QH) state for the experimentally relevant case of an effective constant density (seen by the gate). A direct signature of QAH phase in magnetic fields is a long $\sigma_{xy}= e^2/h$ ($\sigma_{xy}= -e^2/h$) plateau in Cr$_x$(Bi$_{1-y}$Sb$_y$)$_{2-x}$Te$_3$ (HgMnTe quantum wells). Furthermore, we predict a new transition between the quantum spin Hall (QSH) and the QAH state in magnetic fields, for constant effective carrier density, without magnetic impurities but driven by effective g-factors and particle-hole asymmetry. This transition can be related to the stability of edge states in the Dirac mass gap of 2D topological insulators (TIs), even in high magnetic fields. 
Jan B\"ottcher and Ewelina M. Hankiewicz
cond-mat.mes-hall