Research progress of two-dimensional organic topological insulators

The discovery of new materials promotes the progress in science and technique. Among these new materials, topological materials have received much attention in recent years. Topological phases represent the advances both in the fundamental understanding of materials and in the broad applications in spintronics and quantum computing. The two-dimensional (2D) topological insulator (TI), also called quantum spin Hall insulator, is a promising material which has potential applications in future electronic devices with low energy consumption. The 2D TI has a bulk energy gap and a pair of gapless metallic edge states that are protected by the time reversal symmetry. To date, most of topological insulators are inorganic materials. Organic materials have potential advantages of low cost, easy fabrications, and mechanical flexibility. Historically, inorganic materials and devices have always found their organic counterparts, such as organic superconductors, organic light emitting diodes and organic spintronics. Recently, it has been predicted that some metal-organic lattices belong in an interesting class of 2D organic topological insulator (OTI). In this review, we present the progress of OTIs mainly in two typical types of them. In the first group, metal atoms bond with three neighboring molecules to form a hexagonal lattice, while they bond with two neighboring molecules to form a Kagome lattice. The electronic properties show that the Dirac band around Fermi level mainly comes from the hexagonal sites, and the flat band around Fermi level mainly is from Kagome lattice. It has been found that some of the materials from the first group could be intrinsic OTIs. However, none of the 2D OTIs predicted in the second group with a Kagome lattice is intrinsic. To obtain intrinsic OTIs from those non-intrinsic ones, in the heavy doping of material (one or two electrons per unit cell) it is required to move the Fermi level inside the gap opened by spin-orbit coupling, which is hard to realize in experiment. Therefore, many efforts have been made to search for intrinsic OTIs. It has been reported that the first group of 2D OTIs with a hexagonal lattice is found to be more possible to be intrinsic. By performing an electron counting and analyzing the orbital hybridization, an existing experimentally synthesized Cu-dicyanoanthracene (DCA) metal-organic framework is predicted to be an intrinsic OTI. Furthermore, like Cu-DCA, the structures consisting of molecules with cyanogen groups and noble metal atoms could be intrinsic OTIs. Finally, we discuss briefly possible future research directions in experimental synthesis and computational design of topological materials. We envision that OTIs will greatly broaden the scientific and technological influence of topological insulators and become a hot research topic in condensed matter physics.