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arXiv 1203.6340cond-mat.mes-hall
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绝缘双层石墨烯的整数量子霍尔效应理论

Theory of integer quantum Hall effect in insulating bilayer graphene

Bitan Roy

摘要:

提出了量子化磁场作用下绝缘双层石墨烯(BLG)的变分基态。由于塞曼耦合,全带隙BLG中的层反铁磁(LAF)序参量被投影到自旋易平面上,同时铁磁序沿磁场方向发展,并可通过交换作用进一步增强.激活间隙的$ν=0$霍尔状态,然后显示一个交叉从二次线性缩放与磁场,因为它变得更强,我获得了极好的协议与最近的实验与现实的强度为铁磁相互作用。LAF阶的一个分量,平行于外部磁场,在填充$ν=\pm 2$时产生额外的不可压缩霍尔态,而BLG中的远程跳跃产生$ν=\pm 1$霍尔态。LAF的顺序在倾斜磁场中的演变,缩放的间隙在$ν=2$,外部电场对各种霍尔高原的影响,和不同的可能层次的分数量子霍尔状态的突出显示。

英文摘要:

A variational ground state for insulating bilayer graphene (BLG), subject to quantizing magnetic fields, is proposed. Due to the Zeeman coupling, the layer anti-ferromagnet (LAF) order parameter in fully gapped BLG gets projected onto the spin easy plane, and simultaneously a ferromagnet order, which can further be enhanced by exchange interaction, develops in the direction of the magnetic field. The activation gap for the $ν=0$ Hall state then displays a crossover from quadratic to linear scaling with the magnetic field, as it gets stronger, and I obtain excellent agreement with a number of recent experiments with realistic strengths for the ferromagnetic interaction. A component of the LAF order, parallel to the external magnetic field, gives birth to additional incompressible Hall states at filling $ν=\pm 2$, whereas the remote hopping in BLG yields $ν=\pm 1$ Hall states. Evolution of the LAF order in tilted magnetic fields, scaling of the gap at $ν=2$, the effect of external electric fields on various Hall plateaus, and different possible hierarchies of fractional quantum Hall states are highlighted.

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