石墨烯薄片中的电子壳层和超壳层结构
Electronic shell and supershell structure in graphene flakes
摘要：
我们使用一个简单的紧束缚（TB）模型来研究自由石墨烯薄片的电子性质。三角形石墨烯薄片的价电子呈现出壳层和超壳层结构，其解析表达式由三角形空腔的波动方程导出。然而，对于扶手椅形和锯齿形的三角形，该解有不同的选择规则，大约需要40000个原子才能清楚地看到第一次超壳层振荡。在球形薄片的情况下，锯齿形区域的边缘状态主导壳结构，因此壳结构对薄片直径和中心敏感。由于零能带隙，用外部栅极制成的势阱在石墨烯中不能具有真正的束缚态。然而，它可以在导带中引起强共振。
英文摘要：
We use a simple tight-binding (TB) model to study electronic properties of free graphene flakes. Valence electrons of triangular graphene flakes show a shell and supershell structure which follows an analytical expression derived from the solution of the wave equation for triangular cavity. However, the solution has different selection rules for triangles with armchair and zigzag edges, and roughly 40000 atoms are needed to see clearly the first supershell oscillation. In the case of spherical flakes, the edge states of the zigzag regions dominate the shell structure which is thus sensitive to the flake diameter and center. A potential well that is made with external gates cannot have true bound states in graphene due to the zero energy band gap. However, it can cause strong resonances in the conduction band.
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