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arXiv 1709.09010cond-mat.mes-hall
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交流驱动石墨烯中的量子霍尔效应:从半整数到整数

Quantum Hall effect in ac driven graphene: from half-integer to integer case

Kai-He Ding, Lih-King Lim, Gang Su, Zheng-Yu Weng

摘要:

从理论上研究了在交流电场作用下石墨烯的量子霍尔效应。基于紧束缚模型,随着交流电场的增加,半整数霍尔平台在$σ_{xy} = \pm(n + 1/2)4e^2/h$($n$为整数)处的结构随着新的整数霍尔平台在$σ_{xy} = \pm n(4e^2/h)$处的加入而发生了定性的变化,霍尔平台从带中心区的边缘开始向带中心移动.超过临界场强,可以在带中心实现具有$σ_{xy} = 0$的霍尔平台,从而完全恢复具有粒子-空穴对称性的常规整数QHE。在狄拉克锥合并的低能汉密尔顿中,我们与霍尔平台跃迁的紧束缚计算非常一致。我们还获得了驱动石墨烯带的能带结构,以提供对新霍尔平台外观的进一步理解,显示出$σ_{xy} = 0$态的平凡绝缘体行为。在无序的存在下,我们数值研究了有限驱动样本中量子霍尔态的无序诱导破坏,发现在未驱动无序情况下已知的定性特征得以保持。

英文摘要:

We theoretically study the quantum Hall effect (QHE) in graphene with an ac electric field. Based on the tight-binding model, the structure of the half-integer Hall plateaus at $σ_{xy} = \pm(n + 1/2)4e^2/h$ ($n$ is an integer) gets qualitatively changed with the addition of new integer Hall plateaus at $σ_{xy} = \pm n(4e^2/h)$ starting from the edges of the band center regime towards the band center with an increasing ac field. Beyond a critical field strength, a Hall plateau with $σ_{xy} = 0$ can be realized at the band center, hence restoring fully a conventional integer QHE with particle-hole symmetry. Within a low-energy Hamiltonian for Dirac cones merging, we show a very good agreement with the tight-binding calculations for the Hall plateau transitions. We also obtain the band structure for driven graphene ribbons to provide a further understanding on the appearance of the new Hall plateaus, showing a trivial insulator behavior for the $σ_{xy} = 0$ state. In the presence of disorder, we numerically study the disorder-induced destruction of the quantum Hall states in a finite driven sample and find that qualitative features known in the undriven disordered case are maintained.

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