Department of Physics and Nanotechnology, Aalborg University, DK-9220 Aalborg East, Denmark.
ACS Nano. 2011 Jan 25;5(1):523-9. doi: 10.1021/nn102442h. Epub 2010 Dec 16.
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 nonisosceles triangular structures to probe the sensitivity of the gap in triangular lattices to small changes in geometry.
原始石墨烯是一种半导体，因此没有带隙。通过在石墨烯片上制作纳米级周期性孔阵列，可能会形成带隙；通过调整晶格参数可以控制间隙的大小。孔直径、孔几何形状、晶格几何形状和孔的间距都是决定带隙大小的重要参数，对于技术应用，带隙至少应为十分之几电子伏特的数量级。我们研究了四种不同的孔构型：矩形、三角形、旋转三角形和蜂窝晶格。研究发现，晶格几何形状对于带隙的大小起着至关重要的作用：三角形排列总是显示出相当大的带隙，而对于其他类型，只有特定的孔间距才能导致较大的带隙。这一观察结果可以用 Clar 六重体理论来解释，我们发现，产生大带隙的一个充分条件是，六重体的数量超过单位晶胞中六边形总数的三分之一。此外，我们还研究了非等腰三角形结构，以探测三角形晶格中间隙对几何形状微小变化的敏感性。
