周期性交变磁场中的石墨烯：反常霍尔效应的不寻常量子化
Graphene in periodically alternating magnetic field: unusual quantization of the anomalous Hall effect
摘要：
研究了三角晶格对称的石墨烯在周期性零平均磁场中的能谱和电子性质。周期性场导致形成一组由间隙分隔的能带，这些能带可以被外场操纵。用解析和数值方法计算了与电子在$k$空间中运动有关的Berry相和相应的表征能带拓扑的Chern数。在这方面，我们讨论了绝缘态下费米能级位于微间隙中时的反常霍尔效应。计算结果表明，在石墨烯的无隙Dirac谱模型中，反常的霍尔效应可以看作是与不等价的Dirac点有关的分数量子数之和。
英文摘要：
We study the energy spectrum and electronic properties of graphene in a periodic magnetic field of zero average with a symmetry of triangular lattice. The periodic field leads to formation of a set of minibands separated by gaps, which can be manipulated by external field. The Berry phase, related to the motion of electrons in $k$ space, and the corresponding Chern numbers characterizing topology of the energy bands are calculated analytically and numerically. In this connection, we discuss the anomalous Hall effect in the insulating state, when the Fermi level is located in the minigap. The results of calculations show that in the model of gapless Dirac spectrum of graphene the anomalous Hall effect can be treated as a sum of fractional quantum numbers, related to the nonequivalent Dirac points.
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