We calculate one-loop polarization in bilayer graphene in the four-band approximation for arbitrary values of frequency, momentum, and doping. At low and high energy our results reduce to the polarization functions calculated in the two-band approximation and in the case of single-layer graphene, respectively. The special cases of static screening and plasmon modes are analyzed.
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Oleksandr Gamayun (2011) studied this question.
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