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Identification and control of topological phases in topological thin filmsoffer great opportunity for fundamental research and the fabrication oftopology-based devices. Here, combining molecular beam epitaxy, angle-resolvedphotoemission spectroscopy and ab-initio calculations, we investigate theelectronic structure evolution in (Bi1-xInx)2Se3 films with thickness from 2 to13 quintuple layers. We identify several phases with their characteristictopological nature and evolution between them, i.e., dimensional crossover froma three-dimensional topological insulator with gapless surface state to itstwo-dimensional counterpart with gapped surface state, and topological phasetransition from topological insulator to a normal semiconductor with increasingIn concentration x. Furthermore, by introducing In alloying as an external knobof band gap engineering, we experimentally demonstrated the trivial topologicalnature of Bi2Se3 thin films (below 6 quintuple layers) as two-dimensionalgapped systems, in consistent with our theoretical calculations. Our resultsprovide not only a comprehensive phase diagram of (Bi1-xInx)2Se3 and a route tocontrol its phase evolution, but also a practical way to experimentallydetermine the topological properties of a gapped compound by topological phasetransition and band gap engineering.

Dimensional crossover and topological nature of the thin films of a three-dimensional topological insulator by band gap engineering