球上的反常量子霍尔效应
Anomalous Quantum Hall Effect on Sphere
摘要：
我们研究了生活在双球S^2上的相对论粒子在磁场作用下表现出的反常量子霍尔效应。我们首先通过泡利-薛定谔哈密顿量H_{s} ^{SP}在狄拉克和朗道算符之间建立一个直接的联系。这将有助于狄拉克本征值和本征函数的推导。通过对H_{s} ^{SP}谱的分析，我们证明了存在由两个有效磁场支持的复合费米子性质。对于最低的朗道能级，我们认为石墨烯的基本物理性质与二维电子气相似，这与平面极限相一致。对于更高的朗道能级，我们提出了一个SU（N）波函数不同的填充因子，捕捉所有的对称性。重点放在石墨烯的情况下，即N=4，我们给出了不同的配置，允许恢复一些已知的结果。
英文摘要：
We study the anomalous quantum Hall effect exhibited by the relativistic particles living on two-sphere S^2 and submitted to a magnetic monopole. We start by establishing a direct connection between the Dirac and Landau operators through the Pauli--Schrödinger Hamiltonian H_{s}^{SP}. This will be helpful in the sense that the Dirac eigenvalues and eigenfunctions will be easily derived. In analyzing H_{s}^{SP} spectrum, we show that there is a composite fermion nature supported by the presence of two effective magnetic fields. For the lowest Landau level, we argue that the basic physics of graphene is similar to that of two-dimensional electron gas, which is in agreement with the planar limit. For the higher Landau levels, we propose a SU(N) wavefunction for different filling factors that captures all symmetries. Focusing on the graphene case, i.e. N=4, we give different configurations those allowed to recover some known results.
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