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Effects of nonlocal plasmons in gapped graphene micro-ribbon array and 2DEG on near-field electromagnetic response in the deep-subwavelength regime

机译：非局域等离子体在有缺口的石墨烯微带阵列中的应用   关于深亚波长区域中的近场电磁响应的2DEG

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A self-consistent theory involving Maxwell equations and a density-matrixlinear-response theory is solved for an electromagnetically-coupled dopedgraphene micro-ribbon array and a quantum-well electron gas sitting at aninterface between a half-space of air and another half-space of a dopedsemiconductor substrate which supports a surface-plasmon mode in our system.The coupling between a spatially-modulated total electromagnetic field and theelectron dynamics in a Dirac-cone of a graphene ribbon, as well as the couplingof the far-field specular and near-field higher-order diffraction modes, areincluded in the derived electron optical-response function. Full analyticalexpressions are obtained with non-locality for the optical-response functionsof a two-dimensional electron gas and a graphene layer with an induced bandgap,and are employed in our numerical calculations beyond the long-wavelength limit(Drude model). Both the near-field transmissivity and reflectivity spectra, aswell as their dependence on different configurations of our system and on thearray period, ribbon width, graphene chemical potential of quantum-wellelectron gas and bandgap in graphene, are studied. Moreover, the transmittedE-field intensity distribution is calculated to demonstrate its connection tothe mixing of specular and diffraction modes of the total electromagneticfield. An externally-tunable electromagnetic coupling among the surface,conventional electron-gas and massless graphene intraband plasmon excitationsis discovered and explained. Furthermore, a comparison is made between thedependence of the graphene-plasmon energy on the ribbon width and chemicalpotential in this paper and the recent experimental observation given by Ju, etal., [Nature Nanotechnology, 6, 630 (2011)] for a graphene micro-ribbon arrayin the terahertz-frequency range.
机译：解决了一个电磁耦合的掺杂石墨烯微带阵列和一个位于空气半空间与另一个半空间之间的界面的量子阱电子气的涉及麦克斯韦方程和密度矩阵线性响应理论的自洽理论在我们的系统中支持表面等离子体模式的掺杂半导体衬底的研究。空间调制的总电磁场与石墨烯带的狄拉克锥中的电子动力学之间的耦合以及远场镜面和近场的耦合场高阶衍射模式包括在导出的电子光响应函数中。对于二维电子气和具有感应带隙的石墨烯层的光响应函数，获得了非局部的完整解析表达式，并将其用于超出长波长限制的数值计算中（Drude模型）。研究了近场透射率和反射率谱，以及它们对系统不同构型以及阵列周期，带宽度，量子阱电子气体的石墨烯化学势和石墨烯中的带隙的依赖性。此外，计算了透射的电场强度分布，以证明其与总电磁场的镜面反射模式和衍射模式的混合有关。发现并解释了表面，常规电子气和无质量石墨烯带内等离子体激元之间的外部可调电磁耦合。此外，在本文中比较了石墨烯-等离子体激元能量对带宽度和化学势的依赖性以及Ju等人[Nature Nanotechnology，6，630（2011）]最近对石墨烯微粉的实验观察。太赫兹频率范围内的碳带阵列。

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