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

中文翻译：

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用栅极电压控制双层石墨烯中无间隙态的层定位。

在具有堆叠畴壁的门控双层石墨烯中进行的实验显示了无谷混合保护的拓扑无间隙状态。在这里，我们使用原子模型研究了栅极电压下的这些状态，这使我们能够阐明它们的起源。我们发现，栅极电势控制着两个状态的层局部化，这取决于所施加的栅极电压幅度在层之间非平凡地切换。通过分析层之间碳键的形成，我们还显示了这些双层无间隙状态是如何从单层石墨烯的带中产生的。在此分析的基础上，我们提供了具有解析解的哈密顿量模型，该模型将层定位解释为所施加电势与层间跳变之比的函数。我们的结果为操纵电子设备中的无间隙状态开辟了一条道路，