Phonon and defect mediated quantum anomalous Hall insulator to metal transition in magnetically doped topological insulators

Quantum Anomalous Hall (QAH) state in six quintuple layer Cr$_{0.1}$(Bi$_{0.2}$Sb$_{0.8}$)$_{1.9}$Te$_3$ thin films were studied through scanning tunneling spectroscopy (STS) and electrical transport measurements. While the surface state is gapless above the Curie temperature ($T_\mathrm{C} \approx 30$ K), scanning tunneling spectroscopy (STS) of the sample reveals a topologically non-trivial gap with an average value of $\approx 13.5$ meV at 4.2 K below the ferromagnetic transition. Nonetheless, areal STS scans of the magnetic topological insulator exhibit energy modulations on the order of several meV's in the surface bands which result in the valence band maximum in some regions becoming higher than the energy of the conduction band minimum of some other regions that are spatially separated by no more than 3 nm. First principle calculations demonstrate that the origin of the observed inhomogeneous energy band alignment is an outcome of many-body interactions, namely electron-defect interactions and electron-phonon interactions. Defects play the role of locally modifying the energy landscape of surface bands while electron-phonon interactions renormalize the surface bands such that the surface gap becomes reduced by more than 1 meV as temperature is raised from 0 to 4.2 K. These many-body interactions at a finite temperature result in substantial increase of electron tunneling across the spatially separated conduction band pockets even for finite temperatures well below $T_\mathrm{C}$ , thus driving the magnetic topological insulator out of its QAH insulating phase into a metallic phase at a relatively low temperature.