We consider a screened Coulomb interaction between electrons in graphene and determine their dynamic response functions, such as a longitudinal and a transverse electric conductivity and a polarization function and compare them to the corresponding quantities in the short-range interaction model. The calculations are performed to all orders for short-range interaction by taking into account the self-energy renormalization of the electron velocity and using a ladder approximation to account for the vertex corrections, ensuring that the Ward identity (charge conservation law) is satisfied. Our findings predict a resonant response of interacting electron-hole pairs at a particular frequency below the threshold $qv=\omega$ and further predict an instability for sufficiently strong interactions.

中文翻译：

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具有屏蔽库仑和短程相互作用的二维Dirac费米子动力响应函数

我们考虑了石墨烯中电子之间的屏蔽库仑相互作用，并确定了它们的动态响应函数，例如纵向和横向电导率以及极化函数，并将它们与短程相互作用模型中的相应数量进行比较。通过考虑电子速度的自能量重新归一化并使用梯形近似来解决顶点校正，可以对所有短程相互作用的阶次执行计算，从而确保满足Ward身份（电荷守恒律）。我们的发现预测低于阈值的特定频率下相互作用的电子-空穴对的共振响应$qv=\omega$ 并进一步预测足够强的交互作用的不稳定性。