Absence of a Dirac gap in ferromagnetic Cr${}_x$(Bi${}_{0.1}$Sb${}_{0.9}$)${}_{2-x}$Te${}_3$

Magnetism breaks the time reversal symmetry expected to open a Dirac gap in 3D topological insulators that consequently leads to quantum anomalous Hall effect. The most common approach of inducing ferromagnetic state is by doping magnetic 3$d$ elements into bulk of 3D topological insulators. In Cr${}_{0.15}$(Bi${}_{0.1}$Sb${}_{0.9}$)${}_{1.85}$Te${}_3$, the material where the quantum anomalous Hall effect was initially discovered at temperatures much lower than the ferromagnetic transition, $T_C$, the scanning tunneling microscopy studies have reported a large Dirac gap $\sim 20-100$ meV. The discrepancy between the low temperature of quantum anomalous Hall effect ($\ll T_C$)andlargespectroscopicDiracgaps($\gg T_C$) found in magnetic topological insulators remains puzzling. Here, we used angle-resolved photoemission spectroscopy to study the surface electronic structure of pristine and potassium doped surface of Cr${}_{0.15}$(Bi${}_{0.1}$Sb${}_{0.9}$)${}_{1.85}$Te${}_3$. Upon potassium deposition, the $p$-type surface state of pristine sample was turned into an $n$-type, allowing spectroscopic observation of Dirac point. We find a gapless surface state, with no evidence of a large Dirac gap reported in tunneling studies.