Elucidating the physical origin for the disappearance of quantum anomalous Hall (QAHE) effect in Cr-doped (Bi,Sb)₂Te₃ above sub-Kelvin temperatures by transport and scanning tunneling spectroscopic (STS) studies

Experimental observation of the QAHE among Cr-doped (Bi,Sb)₂Te₃, which are magnetic topological insulators (MTIs), has been bound to below sub-Kelvin temperatures. Such limitation of the QAHE imposes an inherent constraint on technological applications, which is unexpected given that these MTIs exhibit long-range ferromagnetic ordering at much higher temperatures: Transport measurements of Cr-doped (Bi,Sb)₂Te₃ have shown bulk Curie temperatures (T_C) ranging from 20 to 30 K, whereas QAHE only occurred below ~ 0.1 K. To shed light on this discrepancy, a combined study of temperature dependent transport and STS measurements in Cr-doped (Bi,Sb)₂Te₃ were performed. Our experimental results revealed that despite a topological gap opening in the surface state of the MTIs below T_C, the presence of a bulk valence band within the similar energy range resulted in an indirect bandgap that may be overcome by thermal excitations, thus corroding the QAHE of the surface state except at very low temperatures. We further provided spectroscopic evidences for homogeneous Cr-doping in the MTIs, indicating that the lack of QAHE was not due to spatially inhomogeneous magnetic order. This work is jointly supported by ARO/MURI (Award #W911NF-16-1-0472) and NSF/IQIM at Caltech (Award #1733907).