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Sudden gap-closure across the topological phase transition in Bi$_{2-x}$In$_{x}$Se$_{3}$

The phase transition from a topological insulator to a trivial band insulator is studied by angle-resoled photoemission spectroscopy on Bi$_{2-x}$In$_{x}$Se$_{3}$ single crystals. We first report the complete evolution of the bulk band structures throughout the transition. The robust surface state and the bulk gap size ($\sim$ 0.50 eV) show no significant change upon doping for $x$ = 0.05, 0.10 and 0.175. At $x$ $\geq$ 0.225, the surface state completely disappears and the bulk gap size increases, suggesting a sudden gap-closure and topological phase transition around $x \sim$ 0.175$-$0.225. We discuss the underlying mechanism of the phase transition, proposing that it is governed by the combined effect of spin-orbit coupling and interactions upon band hybridization. Our study provides a new venue to investigate the mechanism of the topological phase transition induced by non-magnetic impurities.