Topological states in two-dimensional hexagon lattice bilayers

• The system exhibits quantum valley Hall and single-edge quantum valley Hall states.
• The quantum valley Hall and single-edge quantum valley Hall states have different edge modes.
• Providing three ways to control the topological states.

We investigate the topological states of the two-dimensional hexagon lattice bilayer. The system exhibits a quantum valley Hall (QVH) state when the interlayer interaction t⊥t⊥ is smaller than the nearest neighbor hopping energy t  , and then translates to a trivial band insulator state when t⊥/t>1t⊥/t>1. Interestingly, the system is found to be a single-edge QVH state with t⊥/t=1t⊥/t=1. The topological phase transition also can be presented via changing bias voltage and sublattice potential in the system. The QVH states have different edge modes carrying valley current but no net charge current. The bias voltage and external electric field can be tuned easily in experiments, so the present results will provide potential application in valleytronics based on the two-dimensional hexagon lattice.