| Summary: | Topological crystalline insulators (TCI) have been experimentally manufactured and studied. We propose a minimal tight-binding model for thin films made of TCI on the basis of the mirror and discrete rotational symmetries. The basic term consists of the spin–orbit interaction describing a Weyl semimetal, where gapless Dirac cones emerge at all the high-symmetry points in the momentum space. We then introduce the mass term providing gaps to Dirac cones. They simulate the thin films made of the [001], [111] and [110] TCI surfaces. TCI thin films are two-dimensional topological insulators protected by mirror symmetry. The mirror symmetry is broken by introducing an electric field ${{E}_{z}}$ perpendicular to the film. We first note that the band structure can be controlled using the electric field. We then analyze the mirror-Chern number and the edge modes taking into consideration the bulk–edge correspondence, even for ${{E}_{z}}\ne 0$ . We also calculate the conductance as a function of ${{E}_{z}}$ . We propose a multi-digit topological field-effect transistor by applying an electric field independently to the right and left edges of a nanoribbon. Our results will open up a new route to topological electronics.
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