Gate-induced localized states along armchair chain in graphene

In this presentation, we show that a gate-induced line potential in the armchair-chain direction (along y) on a graphene sheet gives rise to localized states. The generation of these localized states is found once the gate-induced potential V₀ becomes nonzero. This is demonstrated, for a nonzero k_y , by our two findings: (1) that the two valley-associated evanescent states on one side of the line-potential have their pseudospins lying on the same plane, and their relative pseudospin orientation span the 2π angular space when the energy is scanned across the energy gap for the k_y, and (2) that the boundary condition for the localized states, formulated into an operator connecting the two evanescent states, has the operator being transformed into a rotation operator by a nonzero V₀, with the rotation axis normal to the plane of the pseudospins. Our results reveal that the formation of the localized states is topological.