The effect of magnetic field on electron transport in the inverted band structure of HgTe/CdTe quantum well is investigated. Although magnetic field breaks the time-reversal symmetry, the quantum spin Hall effect can still survive at large magnetic field up to 10 T. Moreover, two quantum anomalous Hall-like phases emerge, in which the system only has a spin-up or spin-down edge state at a given sample edge and the edge current is spin polarized. By tuning the Fermi energy, the system can transit between the quantum spin Hall phase and two quantum anomalous Hall-like phases, so the polarized direction of the edge current is well controllable. Thus the spin selectivity can be realized for potential applications of spintronics. Due to the quantum spin and anomalous Hall-like effects, the longitudinal and Hall resistances exhibit quantum plateaus. In addition, at certain magnetic field, some exotic plateaus like $\frac{2}{3}$ fractional quantum Hall effect are also observed, where edge states with the same spin counterpropagate at the one edge. At last, these plateaus are hardly affected by Rashba spin-orbit interaction, Zeeman effect, and Anderson disorder.

• Received 5 December 2011

DOI:https://doi.org/10.1103/PhysRevB.85.125401