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arXiv 1502.05020cond-mat.mes-hallquant-ph
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石墨烯的边缘磁输运:解析和数值研究的结合

Edge magnetotransport in graphene: A combined analytical and numerical study

Thomas Stegmann, Axel Lorke

摘要:

采用非平衡格林函数方法,对垂直磁场中石墨烯条边界上的电流流动进行了理论研究。在边界处的镜面反射的情况下,霍尔电阻示出等距峰,这是由于经典的回旋运动。当磁场的强度增加时,观察到异常电阻振荡,类似于在非相对论性2D电子气中发现的那些[新。15:113047(2013)]。使用一个简化的模型,它允许解析地解决狄拉克方程,振荡被解释为被占用的边缘状态之间的干扰,导致在霍尔电阻跳动。给出了实验可观测性的经验法则。此外,石墨烯中的局部电流流动受到边界几何形状的显著影响。有限的边缘电流在扶手椅边缘上流动,而在锯齿形边缘上的电流完全消失。在扩散边界散射的情况下,可以观察到量子霍尔阶梯。局部电流中空间分离的边缘通道的数量等于所占用的朗道能级的数量。局域态密度中的边缘通道被模糊了,但如果只考虑碳原子的子集,就可以使其可见。

英文摘要:

The current flow along the boundary of graphene stripes in a perpendicular magnetic field is studied theoretically by the nonequilibrium Green's function method. In the case of specular reflections at the boundary, the Hall resistance shows equidistant peaks, which are due to classical cyclotron motion. When the strength of the magnetic field is increased, anomalous resistance oscillations are observed, similar to those found in a nonrelativistic 2D electron gas [New. J. Phys. 15:113047 (2013)]. Using a simplified model, which allows to solve the Dirac equation analytically, the oscillations are explained by the interference between the occupied edge states causing beatings in the Hall resistance. A rule of thumb is given for the experimental observability. Furthermore, the local current flow in graphene is affected significantly by the boundary geometry. A finite edge current flows on armchair edges, while the current on zigzag edges vanishes completely. The quantum Hall staircase can be observed in the case of diffusive boundary scattering. The number of spatially separated edge channels in the local current equals the number of occupied Landau levels. The edge channels in the local density of states are smeared out but can be made visible if only a subset of the carbon atoms is taken into account.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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