We study the wake effect in a graphene-Al₂O₃-graphene composite system induced by an external charged particle moving parallel to it by using the dynamic polarization function of graphene within the random phase approximation for its π electrons described as Dirac's fermions and by using a local dielectric function for the bulk sapphire (aluminum oxide, Al₂O₃). We explore the effects of variation of the particle speed, its distance from the top graphene layer, the thickness of the Al₂O₃ layer, the damping rate of plasmons in graphene, and the doping density (i.e., Fermi energy) of graphene on the wake potential. For the velocity of the charged particle below the threshold for excitations of the Dirac plasmon in graphene, given by its Fermi velocity $v_F$, strong effects are observed due to variation of the particle distance, while for the velocity of the charged particle above $v_F$ strong effects are observed due to varying the thickness of the Al₂O₃ layer, as well as due to plasmon damping of graphene's π electrons, and graphene doping.

我们利用石墨烯在其π电子的随机相近似内的动态极化函数来描述由外部平行的带电粒子引起的石墨烯-Al ₂ O _3-石墨烯复合系统中的尾流效应，该π电子被描述为狄拉克费米子，并且通过对块状蓝宝石（氧化铝，Al ₂ O ₃）使用局部介电函数。我们探索了颗粒速度变化，其与顶层石墨烯层的距离，Al ₂ O ₃厚度的影响。层，石墨烯中等离激元的阻尼率以及石墨烯在唤醒电势上的掺杂密度（即费米能）。对于带电粒子的速度低于石墨烯中狄拉克等离子体激元激发的阈值，由费米速度给出$v_F$，由于粒子距离的变化，观察到了强烈的影响，而对于上述带电粒子的速度 $v_F$由于改变了Al ₂ O ₃层的厚度，以及由于石墨烯π电子的等离激元阻尼和石墨烯掺杂，观察到了强烈的效果。