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.

• Received 24 April 2020
• Revised 25 August 2020
• Accepted 25 August 2020

DOI:https://doi.org/10.1103/PhysRevB.102.125421