三角形、矩形和蜂窝状石墨烯反点晶格的Clar六重态分析
Clar Sextet Analysis of Triangular, Rectangular and Honeycomb Graphene Antidot Lattices
摘要：
原始石墨烯是一种半金属，因此没有带隙。通过在石墨烯片中制造纳米级周期性孔阵列，可以形成带隙;通过调整晶格的参数可以控制带隙的大小。孔直径、孔几何形状、晶格几何形状和孔的间隔是在确定带隙的尺寸中都起重要作用的参数，对于技术应用，带隙的尺寸应当至少为十分之一eV的量级。我们研究了四种不同的孔结构：矩形，三角形，旋转三角形和蜂窝晶格。结果发现，晶格的几何形状起着至关重要的作用的带隙的大小：三角形的安排总是显示一个相当大的差距，而对于其他类型只有特定的孔分离导致一个大的差距。我们用Clar六重态理论解释了这一现象，发现六重态的数量超过晶胞中六边形总数的三分之一是大间隙的充分条件。此外，我们研究非等腰三角形结构，以探讨三角形晶格中的间隙对几何形状的微小变化的敏感性。
英文摘要：
Pristine graphene is a semimetal and thus does not have a band gap. By making a nanometer scale periodic array of holes in the graphene sheet a band gap may form; the size of the gap is controllable by adjusting the parameters of the lattice. The hole diameter, hole geometry, lattice geometry and the separation of the holes are parameters that all play an important role in determining the size of the band gap, which, for technological applications, should be at least of the order of tenths of an eV. We investigate four different hole configurations: the rectangular, the triangular, the rotated triangular and the honeycomb lattice. It is found that the lattice geometry plays a crucial role for size of the band gap: the triangular arrangement displays always a sizable gap, while for the other types only particular hole separations lead to a large gap. This observation is explained using Clar sextet theory, and we find that a sufficient condition for a large gap is that the number of sextets exceeds one third of the total number of hexagons in the unit cell. Furthermore, we investigate non-isosceles triangular structures to probe the sensitivity of the gap in triangular lattices to small changes in geometry.
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