SU的费米子Chern-Simons理论（4）分数量子霍尔效应
Fermionic Chern-Simons Theory of SU(4) Fractional Quantum Hall Effect
摘要：
我们发展了一个基于自旋自由度和谷自由度的SU（4）对称单层石墨烯中分数量子霍尔效应的费米陈-西蒙斯（CS）理论，该理论涉及四个不同的CS规范场.我们选择CS耦合矩阵的相应元素，使得偶数个自旋和谷量子数相关的通量量子附着到所有电子，并且具有给定自旋和谷量子数的任何电子看到附着到具有不同（自旋和谷）量子数的其他电子的整数个通量。使用这个CS矩阵，我们得到了一个可能发生在石墨烯中的分数量子霍尔态的列表，并提出了这些状态的波函数。我们的分析也适用于分数量子霍尔态的双层量子霍尔系统没有自旋极化和双层自旋极化石墨烯。
英文摘要：
We develop a Fermionic Chern-Simons (CS) theory for the fractional quantum Hall effect in monolayer graphene with SU(4) symmetry, arising from the spin and the valley degrees of freedom, which involves four distinct CS gauge fields. We choose the corresponding elements of the CS coupling matrix such that an even number of spin and valley quantum number dependent flux quanta is attached to all electrons and that any electron with a given spin and valley quantum number sees an integer number of flux attached to other electrons with different (spin and valley) quantum numbers. Using this CS matrix, we obtain a list of possible fractional quantum Hall states that might occur in graphene and propose wavefunctions for those states. Our analysis also applies to fractional quantum Hall states of both bilayer quantum Hall systems without spin polarization and bilayer spin polarized graphene.
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