In this paper, we compare the spectra of bulk and edge Hamiltonians on graphene from the point of view of the theory of quantum graphs. Since the bulk Hamiltonians with even potentials on the graphene has been studied by Kuchment and Post, our main targets here are the edge Hamiltonians on the graphene with boundaries. In this paper, we obtain their spectral properties under the Dirichlet boundary condition on the zigzag edges and draw pictures of the dispersion relation. Then, we obtain the existence of embedded eigenvalues for edge states in spectral bands.

中文翻译：

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曲折边界的石墨烯上Schrödinger方程的边缘状态

在本文中，我们从量子图论的角度比较了石墨烯上的体哈密顿量和边缘哈密顿量的光谱。由于Kuchment和Post已研究了在石墨烯上具有均匀电势的整体哈密顿量，因此我们的主要目标是在石墨烯上具有边界的边缘哈密顿量。在本文中，我们获得了在锯齿形边缘Dirichlet边界条件下的光谱性质，并绘制了色散关系图。然后，我们获得了光谱带边缘状态的嵌入特征值的存在。