Starting from the zero modes of the single and bilayer graphene Hamiltonians we develop a mechanism to construct the eigenstates and eigenenergies for Landau levels in noncommutative plane. General formulas for the spectrum of energies are deduced, for both cases, single and bilayer graphene. In both cases we find that the effect to introduce noncommutative coordinates is a shift in the energy spectrum with respect to result obtained in commutative space.

中文翻译：

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非对易平面中石墨烯层的朗道能级

从单层和双层石墨烯哈密顿量的零模式开始，我们开发了一种机制来构建非交换平面中朗道能级的本征态和本征能。对于单层和双层石墨烯这两种情况，都推导出了能量谱的一般公式。在这两种情况下，我们发现引入非交换坐标的效果是能量谱相对于在交换空间中获得的结果的偏移。