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arXiv 0810.1494cond-mat.mes-hall
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双层石墨烯中的量子霍尔效应:无序效应和量子相变

Quantum Hall Effect in Bilayer Graphene: Disorder Effect and Quantum Phase Transition

R. Ma, L. Sheng, R. Shen, M. Liu, D. N. Sheng

摘要:

基于紧束缚模型,数值研究了无序条件下双层石墨烯中的量子霍尔效应.在由非量子化霍尔效应的临界区分隔的全能带中,确定了两个不同的QHE区域。在能带中心(狄拉克点)附近的霍尔电导率显示出与谷简并度成正比的反常量子化,但$ν=0$平台明显不存在,这与实验观察一致。当存在无序时,扩展能级向能带中心的上浮会破坏霍尔平台,高平台首先消失。围绕带中心的中心两个平台对无序散射是最鲁棒的,其被在其间靠近狄拉克点的小临界区域分开。狄拉克点周围的纵向电导被证明是在一个范围内的无序强度几乎是一个常数,直到最后两个QHE高原完全崩溃。

英文摘要:

We numerically study the quantum Hall effect (QHE) in bilayer graphene based on tight-binding model in the presence of disorder. Two distinct QHE regimes are identified in the full energy band separated by a critical region with non-quantized Hall Effect. The Hall conductivity around the band center (Dirac point) shows an anomalous quantization proportional to the valley degeneracy, but the $ν=0$ plateau is markedly absent, which is in agreement with experimental observation. In the presence of disorder, the Hall plateaus can be destroyed through the float-up of extended levels toward the band center and higher plateaus disappear first. The central two plateaus around the band center are most robust against disorder scattering, which is separated by a small critical region in between near the Dirac point. The longitudinal conductance around the Dirac point is shown to be nearly a constant in a range of disorder strength, till the last two QHE plateaus completely collapse.

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