Abstract
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 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 . We also calculate the conductance as a function of . 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.
Highlights
We propose a minimal tight-binding model for thin films made of topological crystalline insulator (TCI) on the basis of the mirror and discrete rotational symmetries
It is important and urgent to make a further investigation of a TCI thin film, since it may well be a good candidate for designing nanodevices in topological electronics
The aim of this work is to explore the physics of the TCI thin film by constructing a minimal tight-binding model based on the discrete rotation symmetry CN and the mirror symmetry about the 2D plane
Summary
We propose a minimal tight-binding model for thin films made of topological crystalline insulator (TCI) on the basis of the mirror and discrete rotational symmetries. There are yet no experimental measurements, theoretical studies[13,14] have been presented on the thin film made of a TCI It is characterized by the same discrete rotation symmetry CN , and by the mirror symmetry about the 2D plane. A prominent feature is that we can break the mirror symmetry by applying external electric field This is highly contrasted to the case of the time-reversal invariant topological insulator, where the timereversal breaking should be caused by magnetic field or exchange field induced by ferromagnet. The aim of this work is to explore the physics of the TCI thin film by constructing a minimal tight-binding model based on the discrete rotation symmetry CN and the mirror symmetry about the 2D plane. The tight-binding model is useful to analyze the edge states, which transport the ordinary electric current reflecting the topological properties of the thin film
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