New 2D massless Dirac fermion systems and quantum spin Hall insulators based on sp–sp² carbon sheets

Graphene was 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 on its application for quantum computing and spintronics. Nevertheless, the SOC strength of graphene is too small (~40 µeV) to induce the topological insulator phase in an experimentally achievable temperature regime. Here, we design two-dimensional sp–sp² hybrid carbon sheets to discover new Dirac systems, hosting the QSH phase. We find that 21 out of 31 new carbon sheets are identified as Dirac fermion systems without SOC, distinct from graphene in the number, shape, occurring Dirac cones. Furthermore, we find 19 out of the 21 new Dirac fermion systems become QSH insulators with a sizable SOC gap. It is enhanced up to an order of meV, allowing for the QSH effect at experimentally accessible temperatures. Besides, based on the 26 Dirac fermion systems, we find a correlation between the number of Dirac points without SOC and the resultant QSH phase. We hope our findings contribute to new prospects for the design of topological materials with desired properties.