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Experiments in gated bilayer graphene with stacking domain walls presenttopological gapless states protected by no-valley mixing. Here we researchthese states under gate voltages using atomistic models, which allow us toelucidate their origin. We find that the gate potential controls the layerlocalization of the two states, which switches non-trivially between layersdepending on the applied gate voltage magnitude. We also show how these bilayergapless states arise from bands of single-layer graphene by analyzing theformation of carbon bonds between layers. Based on this analysis we provide amodel Hamiltonian with analytical solutions, which explains the layerlocalization as a function of the ratio between the applied potential andinterlayer hopping. Our results open a route for the manipulation of gaplessstates in electronic devices, analogous to the proposed writing and readingmemories in topological insulators.

Controlling the layer localization of gapless states in bilayer graphene with a gate voltage