存在强点缺陷时石墨烯的态密度
Density of states of a graphene in the presence of strong point defects
摘要：
计算了石墨烯中随机位置的强点缺陷引起的零能量附近的态密度。我们不直接研究态密度，而是在幺正极限下分析逆T矩阵的本征函数。基于数值模拟，我们发现逆T矩阵的本征函数的平方幅值在缺陷位置上表现出随机行走行为。因此，本征函数的平方幅度具有相等的{ \it先验}概率，这进一步意味着态密度由众所周知的M-P分布表征。在相应的逆T-矩阵的复场论的鞍点极限下，进一步导出了M-P分布的数值结果。此外，还研究了由于在零能量附近的发散性，P-P分布对石墨烯的磁性和输运性质的影响。
英文摘要：
The density of states near zero energy in a graphene due to strong point defects with random positions are computed. Instead of focusing on density of states directly, we analyze eigenfunctions of inverse T-matrix in the unitary limit. Based on numerical simulations, we find that the squared magnitudes of eigenfunctions for the inverse T-matrix show random-walk behavior on defect positions. As a result, squared magnitudes of eigenfunctions have equal {\it a priori} probabilities, which further implies that the density of states is characterized by the well-known Thomas-Porter type distribution. The numerical findings of Thomas-Porter type distribution is further derived in the saddle-point limit of the corresponding replica field theory of inverse T-matrix. Furthermore, the influences of the Thomas-Porter distribution on magnetic and transport properties of a graphene, due to its divergence near zero energy, are also examined.
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