Many-body effects in graphene beyond the Dirac model with Coulomb interaction

TL;DR

This paper develops a perturbation theory for finite-size graphene sheets considering Coulomb interactions, calculating one-loop corrections to key electronic properties at finite temperature and chemical potential.

Contribution

It introduces a perturbation framework based on the tight-binding Hamiltonian for graphene with arbitrary electron interactions, extending beyond the Dirac approximation.

Findings

Derived one-loop corrections to electron propagator and interaction potential.

Calculated the energy spectrum, Fermi velocity renormalization, and dielectric permittivity.

Provided formulas applicable at finite temperature and chemical potential.

Abstract

This paper is devoted to development of perturbation theory for studying the properties of graphene sheet of finite size, at nonzero temperature and chemical potential. The perturbation theory is based on the tight-binding Hamiltonian and arbitrary interaction potential between electrons, which is considered as a perturbation. One-loop corrections to the electron propagator and to the interaction potential at nonzero temperature and chemical potential are calculated. One-loop formulas for the energy spectrum of electrons in graphene, for the renormalized Fermi velocity and also for the dielectric permittivity are derived.