方形石墨烯量子点电子态和磁性的Dirac方程描述
Dirac equation description on the electronic states and magnetic properties of a square graphene quantum dot
摘要：
在Dirac方程的理论框架下，推导了锯齿形和扶手椅形两种边缘的正方形石墨烯量子点（GQD）的电子本征态.我们发现，狄拉克方程可以确定本征能谱的GQD的高精度，即使它的尺寸减少到几个纳米。更重要的是，从狄拉克方程的描述，我们可以很容易地计算出共轭表面态的数量和能隙，这是密切相关的GQD的磁性。利用Hartree-Fock平均场方法，我们研究了这种正方形GQD中磁有序结构的尺寸依赖性。我们发现，存在一个临界大小的宽度之间的两个锯齿形边缘，以指示开始稳定的磁有序。另一方面，当这种宽度进一步增加时，电荷中性GQD的磁基态能量趋于饱和值。这些结果与第一性原理计算的结果一致。然后，基于Dirac方程关于表面态的解，我们建立了一个简单的两态模型，该模型可以定量地解释正方形GQD中磁有序的尺寸依赖性。
英文摘要：
Electronic eigen-states of a square graphene quantum dot(GQD) terminated by both zigzag and armchair edges are derived in the theoretical framework of Dirac equation. We find that the Dirac equation can determine the eigen-energy 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 principle 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.
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