Tang Changlin, Yan Weihua, Zheng Yisong, Li Guangshe, Li Liping
National Laboratory of Superhard Materials, Department of Physics, Jilin University, Changchun 130023, People's Republic of China. State Key Lab of Structural Chemistry, Fujian Institute of Research on the Structure of Matter and Graduate School of Chinese Academy of Sciences, Fuzhou 350002, People's Republic of China.
Nanotechnology. 2008 Oct 29;19(43):435401. doi: 10.1088/0957-4484/19/43/435401. Epub 2008 Sep 22.
Electronic eigenstates of a square graphene quantum dot (GQD) terminated by both zigzag and armchair edges are derived in the theoretical framework of the Dirac equation. We find that the Dirac equation can determine the eigenenergy spectrum of a GQD with high accuracy even if its size is reduced to a few nanometers. More importantly, from the Dirac equation description we can readily work out the number and energy gap of the conjugate surface states, which are intimately associated with the magnetic properties of the GQD. By using the Hartree-Fock mean field approach, we study the size dependence of the magnetic ordering formation in this square GQD. We find that there exists a critical size of the width between the two zigzag edges to indicate the onset of the stable magnetic ordering. On the other hand, when such a width increases further, the magnetic ground state energy of a charge neutral GQD tends to a saturated value. These results coincide with the previous results obtained from the first-principles calculation. Then, based on the Dirac equation solution about the surface state, we establish a simple two-state model which can quantitatively explain the size dependence of the magnetic ordering in the square GQD.
在狄拉克方程的理论框架下，推导了由锯齿形和扶手椅形边缘终止的方形石墨烯量子点（GQD）的电子本征态。我们发现，即使GQD的尺寸减小到几纳米，狄拉克方程也能高精度地确定其本征能谱。更重要的是，从狄拉克方程描述中，我们可以很容易地算出共轭表面态的数量和能隙，它们与GQD的磁性密切相关。通过使用哈特里 - 福克平均场方法，我们研究了这个方形GQD中磁有序形成的尺寸依赖性。我们发现，在两个锯齿形边缘之间存在一个临界宽度尺寸，以表明稳定磁有序的开始。另一方面，当这样的宽度进一步增加时，电荷中性GQD的磁基态能量趋于饱和值。这些结果与先前从第一性原理计算得到的结果一致。然后，基于关于表面态的狄拉克方程解，我们建立了一个简单的双态模型，该模型可以定量解释方形GQD中磁有序的尺寸依赖性。
