Origin of the low critical observing temperature of the quantum anomalous Hall effect in V-doped (Bi, Sb)₂Te₃ film

The experimental realization of the quantum anomalous Hall (QAH) effect in magnetically-doped (Bi, Sb)₂Te₃ films stands out as a landmark of modern condensed matter physics. However, ultra-low temperatures down to few tens of mK are needed to reach the quantization of Hall resistance, which is two orders of magnitude lower than the ferromagnetic phase transition temperature of the films. Here, we systematically study the band structure of V-doped (Bi, Sb)₂Te₃ thin films by angle-resolved photoemission spectroscopy (ARPES) and show unambiguously that the bulk valence band (BVB) maximum lies higher in energy than the surface state Dirac point. Finally, our results demonstrate clear evidence that localization of BVB carriers plays an active role and can account for the temperature discrepancy.