Graphene has many unique properties which have made it a hotbed of scientific research in recent years. However, it is not expected intuitively that the strong effects of the substrate and Coulomb doping in the center of crystal cell on the polaron in monolayer graphene. Here, the interaction energy of surface electron (hole) in the graphene and optical phonons in the substrate, which give rise to weakly coupled polarons, is analyzed in the context of the Coulomb doping. The ground-state energy of the polaron is calculated using the Lee-Low-Pine unitary transformation and linear combination operator method. It is found that the ground-state energy is an increasing function of magnetic field strength, the bound Coulomb potential, and the cutoff wavenumber. Numerical results also reveal that the ground-state energy reduces as the distance between the graphene and the substrate is increased. Moreover, the ground energy level of polaron shows the two (+) and (−) branches and zero-Landau energy (ground) level separation in the graphene-substrate material.

中文翻译：

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石墨烯-基底对弱耦合束缚磁极化子特性的影响

石墨烯具有许多独特的性质，使其成为近年来科学研究的温床。然而，不能直观地预料到衬底和晶胞中心的库仑掺杂对单层石墨烯中的极化子的强烈影响。在这里，在库仑掺杂的背景下分析了石墨烯中的表面电子（空穴）和基板中的光学声子的相互作用能，这会产生弱耦合极化子。极化子的基态能量使用 Lee-Low-Pine 酉变换和线性组合算子方法计算。发现基态能量是磁场强度、束缚库仑势和截止波数的增函数。数值结果还表明，基态能量随着石墨烯和衬底之间距离的增加而降低。此外，极化子的基能级显示出石墨烯-衬底材料中的两个 (+) 和 (-) 分支和零朗道能量（基）能级分离。