LAUSR

Grapheneis a massless Dirac fermion system, featuring Dirac points in momentum space. It was also first identified as a quantum spin Hall (QSH) insulator when considering spin–orbit coupling (SOC), which opens a band gap at the Dirac points. This discovery has initiated new research efforts to study the QSH effect, towards its application for quantum computing and spintronics. Although the QSH effect has been observed in HgTe quantum wells, the SOC strength of graphene is too small (~1 µeV) to induce the topological insulator phase in an experimentally achievable temperature regime. Here, we perform a systematic atomistic simulation to design two-dimensional sp–sp2 hybrid carbon sheets to discover new Dirac systems, hosting the QSH phase. 21 out of 31 newly discovered carbon sheets are identified as Dirac fermion systems without SOC, distinct from graphene in the number, shape, and position of the Dirac cones occurring in the Brillouin zone. Moreover, we find 19 out of the 21 new Dirac fermion systems become QSH insulators with a sizable SOC gap enhanced up to an order of meV, thus allowing for the QSH effect at experimentally accessible temperatures. In addition, based on the 26 Dirac fermion systems, we make a connection between the number of Dirac points without SOC and the resultant QSH phase in the presence of SOC. Our findings present new prospects for the design of topological materials with desired properties.Atomistic simulations: design of two-dimensional carbon-based Dirac materialsA variety of carbon-based systems with massless Dirac cones can be predicted by first principles. A team led by Hoonkyung Lee at Konkuk University performed a systematic structure search and geometry optimization using atomistic simulations, to explore and design atomically thin carbon materials capable of hosting a quantum spin Hall phase. Starting from two-dimensional sp2–sp2 hybrid networks, the atomistic simulations provided thirty-one carbon sheets featuring various types of massless Dirac-cone systems, including isotropic or anisotropic Dirac cones, and coexisting asymmetric Dirac cones with different anisotropic directions. Furthermore, twenty-one systems were found to host Dirac fermions without spin-orbit coupling, and nineteen of these may become quantum spin Hall insulators with a sizeable spin-orbit coupling. These results highlight a feasible route towards Dirac cone engineering in two-dimensional materials.