Intrinsic Zeeman Effect in Graphene
Intrinsic Zeeman Effect in Graphene
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DOI：
10.1143/jpsj.76.094701
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发表时间：
2007-07
影响因子：
1.7
通讯作者：
M. Ezawa
中科院分区：
文献类型：
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作者：
M. Ezawa
固有塞曼能量正好是石墨烯中电子回旋能量的一半。结果，朗道能级混合发生，以产生由j层石墨烯中的4个j倍简并零能级和4倍简并非零能级组成的能谱，其中对于单层、双层和三层，j分别= 1、2、3。简并性表现在量子霍尔（QH）效应中。我们研究了简并度是如何被库仑相互作用去除的。相对于零能级，激子能隙通过在填充因子ν=0处进行电子-空穴对的BCS型凝聚而打开。单层石墨烯在ν=±1时，双层石墨烯在ν= ±1，±3时，三层石墨烯在ν = ± 1，±3，±5时，由零能简并产生Ising QH铁磁体.对于非零能级，由于单个能级包含不同自旋的上自旋和下自旋电子，因此导出了有效库仑势依赖于自旋的显著结果。
The intrinsic Zeeman energy is precisely one half of the cyclotron energy for electrons in graphene. As a result a Landau-level mixing occurs to create the energy spectrum comprised of the 4 j -fold degenerated zero-energy level and 4-fold degenerated nonzero-energy levels in the j -layer graphene, where j =1,2,3 for monolayer, bilayer and trilayer, respectively. The degeneracy manifests itself in the quantum Hall (QH) effect. We study how the degeneracy is removed by the Coulomb interactions. With respect to the zero-energy level, an excitonic gap opens by making a BCS-type condensation of electron–hole pairs at the filling factor ν=0. It gives birth to the Ising QH ferromagnet at ν=±1 for monolayer, ν=±1,±3 for bilayer, and ν=±1,±3,±5 for trilayer graphene from the zero-energy degeneracy. With respect to the nonzero-energy level, a remarkable consequence is derived that the effective Coulomb potential depends on spins, since a single energy level contains up-spin and down-spin electrons belonging to dif...