Fundamentals and functionalities of silicene, germanene, and stanene

Two-dimensional elemental topological insulators including silicene, germanene and stanene are currently the hottest topics in condensed matter physics. We first review the recent progress on electronic and topological properties of their monolayers from a fundamental viewpoint. Next, we describe their experimental realizations by epitaxial growth and their actual physical properties. We start with the description of the topological nature of generic Dirac systems and then apply it to silicene by introducing the spin and valley degrees of freedom. Based on them, we classify all topological insulators in the general honeycomb system. We discuss topological electronics based on honeycomb systems. We introduce the topological Kirchhoff law, which is a conservation law of topological edge states. A field effect topological transistor is proposed based on the topological edge states. We show that the conductance is quantized even in the presence of random distributed impurities. Monolayer topological insulators will be a key for future topological electronics and spin-valleytronics. The outstanding example of the realization of such monolayer Si, Ge and Sn novel artificial allotropes is the canonical 3 × 3 reconstructed epitaxial silicene phase grown in situ under ultra-high vacuum on the silver (111) surface. Its realization in 2012 has preceded the synthesis of germanene, followed by that of stanene, respectively on Au(111) and Bi2Te3 substrates. Further growth of Si and Ge over monolayer epitaxial silicene and germanene leads to layered thin films displaying Dirac fermion characteristics. Amazingly, Si deposition onto Ag(110) templates yields massively parallel, pentasilicene-like nanoribbons, a novel form of one-dimensional silicon. Field Effect Transistors have been already fabricated both with single and multi-layer silicene channels, clearly demonstrating potential applications in electronics of silicene and such related materials, which are directly compatible with the current, ubiquitous, Si-based technology. Finally, enticing prospects are outlined.