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\nCr$_{0.1}$(Bi$_{0.2}$Sb$_{0.8}$)$_{1.9}$Te$_3$ thin films were studied through\nscanning tunneling spectroscopy (STS) and electrical transport measurements.\nWhile the surface state is gapless above the Curie temperature ($T_\\mathrm{C}\n\\approx 30$ K), scanning tunneling spectroscopy (STS) of the sample reveals a\ntopologically non-trivial gap with an average value of $\\approx 13.5$ meV at\n4.2 K below the ferromagnetic transition. Nonetheless, areal STS scans of the\nmagnetic topological insulator exhibit energy modulations on the order of\nseveral meV's in the surface bands which result in the valence band maximum in\nsome regions becoming higher than the energy of the conduction band minimum of\nsome other regions that are spatially separated by no more than 3 nm. First\nprinciple calculations demonstrate that the origin of the observed\ninhomogeneous energy band alignment is an outcome of many-body interactions,\nnamely electron-defect interactions and electron-phonon interactions. Defects\nplay the role of locally modifying the energy landscape of surface bands while\nelectron-phonon interactions renormalize the surface bands such that the\nsurface gap becomes reduced by more than 1 meV as temperature is raised from 0\nto 4.2 K. These many-body interactions at a finite temperature result in\nsubstantial increase of electron tunneling across the spatially separated\nconduction band pockets even for finite temperatures well below $T_\\mathrm{C}$\n, thus driving the magnetic topological insulator out of its QAH insulating\nphase into a metallic phase at a relatively low temperature.\n