Quantum Spin Hall Phases in Graphene and the Atomically Thin Transition Metal Dichalcogenide Family

The quantum-spin-Hall (QSH) phase with helical edge spin states, in which opposite-moment electron spins counter-propagate within a topologically preserved time reversal symmetry, is attracting considerable attention. The helical edge spin currents allow zero-emission energy spintronic-devices with small error rates by modulating with external bias voltages. Recently, QSH phases and possible 2D topological insulating states have been reported in various atomically thin layers (such as graphene and the transition metal dichalcogenide family). Particularly, (twisted) bi-layer graphene on heavy substrates is becoming a novel candidate for robust QSH phases (including Chern insulating phases), nevertheless, graphene itself lacks spin-orbit coupling owing to the light carbon atoms. Here, research of QSH phases focusing on graphene is reviewed, particularly for using heavy adatom decoration and heavy substrates. They will open the door to next-generation spintronic architectures.