Hall viscosity and electromagnetic response of electrons in graphene
Hall viscosity and electromagnetic response of electrons in graphene
复制标题
石墨烯中电子的霍尔粘度和电磁响应
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
G. Vignale
中科院分区：
文献类型：
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作者：
M. Sherafati;A. Principi;G. Vignale
我们推导了在垂直磁场存在下，单个石墨烯层中非相互作用电子的几何霍尔粘度的解析表达式。我们证明了[C]中最近导出的公式。Hoyos和d.t. Son，物理学家。启。{f 108}, 066805(2012)]，将二维电子气体（2DEG）的霍尔电导率的波向量展开中的q^2$系数sigma_{xy}(q)$与该系统的霍尔粘度和轨道抗磁化率联系起来，继续适用于石墨烯-尽管缺乏伽利略不变性-具有适当的有效质量定义。我们还表明，对于正能量区中足够多的占据朗道能级，石墨烯中电子的霍尔电导率降低到伽利略不变的2DEG，有效质量为$hbar k_F/v_F$（回旋质量）。即使在最苛刻的情况下，即当化学势落在第0和第1朗道能级之间时，回旋加速器质量公式给出的结果也精确到优于1$\%$。霍尔电导率和粘度之间的联系为测量石墨烯中的霍尔粘度提供了一种可能的途径。
We derive an analytic expression for the geometric Hall viscosity of non-interacting electrons in a single graphene layer in the presence of a perpendicular magnetic field. We show that a recently-derived formula in [C. Hoyos and D. T. Son, Phys. Rev. Lett. {f 108}, 066805 (2012)], which connects the coefficient of $q^2$ in the wave vector expansion of the Hall conductivity $sigma_{xy}(q)$ of the two-dimensional electron gas (2DEG) to the Hall viscosity and the orbital diamagnetic susceptibility of that system, continues to hold for graphene -- in spite of the lack of Galilean invariance -- with a suitable definition of the effective mass. We also show that, for a sufficiently large number of occupied Landau levels in the positive energy sector, the Hall conductivity of electrons in graphene reduces to that of a Galilean-invariant 2DEG with an effective mass given by $hbar k_F/v_F$ (cyclotron mass). Even in the most demanding case, i.e. when the chemical potential falls between the zero-th and the first Landau level, the cyclotron mass formula gives results accurate to better than 1$\%$. The connection between the Hall conductivity and the viscosity provides a possible avenue to measure the Hall viscosity in graphene.