Kim S C, Jeong Y H, Yang S-R Eric
J Nanosci Nanotechnol. 2015 Oct;15(10):8263-6. doi: 10.1166/jnn.2015.11251.
Graphene Landau levels have discrete energies consisting zero energy chiral states and non-zero energy states with mixed chirality. Each Landau level splits into discrete energies when a localized potential is present. A simple scaling analysis suggests that a localized potential can act as a strong perturbation, and that it can be even more singular in graphene than in ordinary two-dimensional systems of massful electrons. Parabolic, Coulomb, and Gaussian potentials in graphene may have anomalous boundstates whose probability density has a sharp peak inside the potential and a broad peak of size magnetic length l outside the potential. The n = 0 Landau level with zero energy has only one anomalous state while the n = ±1 Landau levels with non-zero energy have two (integer quantum number n is related to the quantized Landau level energies). These anomalous states can provide a new magnetospectroscopic feature in impurity cyclotron resonances of graphene. In the present work we investigate quantitatively the conditions under which the anomalous states can exist. These results may provide a guide in searching for anomalous states experimentally.
石墨烯朗道能级具有离散能量，由零能量手性态和具有混合手性的非零能量态组成。当存在局域势时，每个朗道能级会分裂为离散能量。一个简单的标度分析表明，局域势可以作为一种强微扰，并且在石墨烯中它可能比在有质量电子的普通二维系统中更加奇异。石墨烯中的抛物线势、库仑势和高斯势可能具有反常束缚态，其概率密度在势内有一个尖锐峰值，在势外有一个大小为磁长度l的宽峰值。能量为零的n = 0朗道能级只有一个反常态，而能量非零的n = ±1朗道能级有两个反常态（整数量子数n与量子化的朗道能级能量相关）。这些反常态可以在石墨烯的杂质回旋共振中提供一种新的磁光谱特征。在本工作中，我们定量研究了反常态能够存在的条件。这些结果可能为实验上寻找反常态提供指导。
