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Topological insulators are a class of band insulators with non-trivialtopology, a result of band inversion due to the strong spin-orbit coupling. Thetransition between topological and normal insulator can be realized by tuningthe spin-orbit coupling strength, and has been observed experimentally.However, the impact of chemical disorders on the topological phase transitionwas not addressed in previous studies. Herein, we report a systematic scanningtunneling microscopy/spectroscopy and first-principles study of the topologicalphase transition in single crystals of In doped Bi$_2$Se$_3$. Surprisingly, noband gap closure was observed across the transition. Furthermore, ourspectroscopic-imaging results reveal that In defects are extremely effective"suppressors" of the band inversion, which leads to microscopic phaseseparation of topological-insulator-like and normal-insulator-like nano regionsacross the "transition". The observed topological electronic inhomogeneitydemonstrates the significant impact of chemical disorders in topologicalmaterials, shedding new light on the fundamental understanding of topologicalphase transition.

Topological phase transition with nanoscale inhomogeneity in (Bi$_{1-x}$In$_{x}$)$_{2}$Se$_{3}$