从指数定理看各种石墨烯构型的零模
Zero modes of various graphene configurations from the index theorem
摘要：
在这篇文章中，我们考虑了一个石墨烯片，折叠在各种紧凑的几何形状与任意拓扑结构描述的某个属，$g$。虽然这些系统的哈密顿量定义在格上，但可以取连续极限。得到的类Dirac-like哈密顿量很好地描述了初始系统的低能模。从第一原理出发，我们推导出一个指数定理，对应于这个哈密顿量。该定理将石墨烯片的零能量模式与紧凑晶格的拓扑结构相关联。对于$g=0$和$g=1$，这些结果与富勒烯分子和碳纳米管的分析和数值研究相吻合，而对于更高的值$g$，他们给出了更复杂的分子的预测。
英文摘要：
In this article we consider a graphene sheet that is folded in various compact geometries with arbitrary topology described by a certain genus, $g$. While the Hamiltonian of these systems is defined on a lattice one can take the continuous limit. The obtained Dirac-like Hamiltonian describes well the low energy modes of the initial system. Starting from first principles we derive an index theorem that corresponds to this Hamiltonian. This theorem relates the zero energy modes of the graphene sheet with the topology of the compact lattice. For $g=0$ and $g=1$ these results coincide with the analytical and numerical studies performed for fullerene molecules and carbon nanotubes while for higher values of $g$ they give predictions for more complicated molecules.
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