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Based on first-principles calculations, we find that LiZnBi, a metallic hexagonal $ABC$ compound, can be driven into a Dirac semimetal with a pair of Dirac points by strain. The nontrivial topological nature of the strained LiZnBi is directly demonstrated by calculating its $\mathbb{Z}_2$ index and the surface states, where the Fermi arcs are clearly observed. The low-energy states as well as topological properties are shown to be sensitive to the strain configurations. The finding of Dirac semimetal phase in LiZnBi may intrigue further researches on the topological properties of hexagonal $ABC$ materials and promote new practical applications., 12 pages, 6 figures

Three-dimensional topological Dirac semimetals represent a novel state of quantum matter with exotic electronic properties, in which a pair of Dirac points with a linear dispersion along all momentum directions exists in the bulk. Herein, by using first-principles calculations, we discover the metastable allotropes of Ge and Sn in the staggered layered dumbbell structure, named germancite and stancite, to be Dirac semimetals with a pair of Dirac points on their rotation axis. On the surface parallel to the rotation axis, a pair of topologically nontrivial Fermi arcs are observed and a Lifshitz transition is found by tuning the Fermi level. Furthermore, the quantum thin film of germancite is found to be an intrinsic quantum spin Hall insulator. These discoveries suggest novel physical properties and future applications of the metastable allotrope of Ge and Sn., W.C. and W.D. acknowledge support from the Ministry of Science and Technology of China and theNational Natural Science Foundation of China (Grant No. 11334006). A.R. acknowledges financial support from the European Research Council Grant DYNamo (ERC-2010-AdG No. 267374) Spanish Grants (FIS2010-21282-C02-01), Grupos Consolidados UPV/EHU del Gobierno Vasco (IT578-13), and EC project CRONOS (280879-2 CRONOS CPFP7). P.T. and S.-C.Z. acknowledge NSF under Grant No. DMR-1305677 and FAME, one of six centers of STARnet, a Semiconductor Research Corporation program sponsored by MARCO and DARPA.

Under the terms of the Creative Commons Attribution License 3.0 (CC-BY).-- et al., From density functional theory within the generalized gradient approximation we predict a structure of stanene with dumbbell units (DBs), and show that it is a two-dimensional topological insulator with an inverted band gap which can be tuned by compressive strain. Furthermore, we propose that the boron nitride sheet and reconstructed (2x2) InSb(111) surfaces are ideal substrates for the experimental realization of DB stanene, maintaining its nontrivial topology. Combined with standard semiconductor technologies, such as magnetic doping and electrical gating, the quantum anomalous Hall effect, Chern half metallicity, and topological superconductivity can be realized in DB stanene on those substrates. These properties make the two-dimensional supported stanene a good platform for the study of quantum spin Hall insulators as well as other exotic quantum states of matter., We acknowledge support from the Ministry of Science and Technology of China (Grants No. 2011CB606405 and No. 2011CB921901) and the National Natural Science Foundation of China (Grant No. 11334006). A.R., S.C., and L.X. acknowledge financial support from the European Research Council Grant DYNamo (ERC-2010-AdG No. 267374) Spanish Grants (FIS2010-21282-C02-01), Grupos Consolidados UPV/EHU del Gobierno Vasco (IT578-13), and EC project CRONOS (280879-2 CRONOS CP-FP7.

The low energy physics of both graphene and surface states of three-dimensional topological insulators is described by gapless Dirac fermions with linear dispersion. In this work, we predict the emergence of a "heavy" Dirac fermion in a graphene/topological insulator hetero-junction, where the linear term almost vanishes and the corresponding energy dispersion becomes highly non-linear. By combining {\it ab initio} calculations and an effective low-energy model, we show explicitly how strong hybridization between Dirac fermions in graphene and the surface states of topological insulators can reduce the Fermi velocity of Dirac fermions. Due to the negligible linear term, interaction effects will be greatly enhanced and can drive "heavy" Dirac fermion states into the half quantum Hall state with non-zero Hall conductance., 2 figures