Two-dimensional (2D) topological insulator (TI) have been recognized as a new class of quantum state of matter. They are distinguished from normal 2D insulators with their nontrivial band-structure topology identified by the $Z_2$ number as protected
by time-reversal symmetry (TRS). 2D TIs have intriguing spin-velocity locked conducting edge states and insulating properties in the bulk. In the edge states, the electrons with opposite spins propagate in opposite directions and the backscattering is fully prohibited when the TRS is conserved. This leads to quantized dissipationless two-lane highway for charge and spin transportation and promises potential applications. Up to now, only very few 2D systems have been discovered to possess this property. The lack of suitable material obstructs the further study and application. Here, by using first-principles calculations, we propose that the functionalized MXene with oxygen, M$_2$CO$_2$ (M=W, Mo and Cr), are 2D TIs with the largest gap of 0.194 eV in W case. They are dynamically stable and natively antioxidant. Most importantly, they are very likely to be easily synthesized by recent developed selective chemical etching of transition-metal carbides (MAX phase). This will pave the way to tremendous applications of 2D TIs, such as ideal conducting wire, multifunctional spintronic device, and the realization of topological superconductivity and Majorana modes for quantum computing.
By using first-principles calculation, we have found that a family of 2D transition metal dichalcogenide haeckelites with square-octagonal lattice $MX_2$-4-8 ($M$=Mo, W and $X$=S, Se and Te) can host quantum spin hall effect. The phonon spectra indic
ate that they are dynamically stable and the largest band gap is predicted to be around 54 meV, higher than room temperature. These will pave the way to potential applications of topological insulators. We have also established a simple tight-binding model on a square-like lattice to achieve topological nontrivial quantum states, which extends the study from honeycomb lattice to square-like lattice and broads the potential topological material system greatly.
Graphene, a two dimensional (2D) carbon sheet, acquires many of its amazing properties from the Dirac point nature of its electronic structures with negligible spin-orbit coupling. Extending to 3D space, graphene networks with negative curvature, cal
led Mackay-Terrones crystals (MTC), have been proposed and experimentally explored, yet their topological properties remain to be discovered. Based on the first-principle calculations, we report an all-carbon MTC with topologically non-trivial electronic states by exhibiting node-lines in bulk. When the node-lines are projected on to surfaces to form circles, drumhead like flat surface bands nestled inside of the circles are formed. The bulk node-line can evolve into 3D Dirac point in the absence of inversion symmetry, which has shown its plausible existence in recent experiments.
