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Electron transport properties of a topological insulator Bi$_2$Se$_3$ thinfilm are studied in Hall-bar geometry. The film with a thickness of 10 nm isgrown by van der Waals epitaxy on fluorophlogopite mica and Hall-bar devicesare fabricated from the as-grown film directly on the mica substrate. Weakantilocalization and electron-electron interaction effects are observed andanalyzed at low temperatures. The phase-coherence length extracted from themeasured weak antilocalization characteristics shows a strong power-lawincrease with decreasing temperature and the transport in the film is shown tooccur via coupled multiple (topological surface and bulk states) channels. Theconductivity of the film shows a logarithmically decrease with decreasingtemperature and thus the electron-electron interaction plays a dominant role inquantum corrections to the conductivity of the film at low temperatures.

Weak antilocalization and electron-electron interaction in coupled multiple-channel transport in a Bi$_2$Se$_3$ thin film