Effective field theory, three-loop perturbative expansion, and their experimental implications in graphene many-body effects

Understand

Many-body electron-electron interaction effects are theoretically considered in monolayer graphene from a continuum effective field-theoretic perspective by going beyond the standard leading-order perturbative renormalization group (RG) analysis.

• Given that the bare fine structure constant in graphene is of order unity, which is neither small to justify a perturbative expansion nor large enough for strong-coupling theories to be applicable, the problem is a difficult one, with some similarity to 2+1-dimensional strong-coupling quantum electrodynamics (QED).
• In this work, we take a systematic and comprehensive analytical approach, working primarily at the Dirac point (intrinsic graphene), by going up to three loops in the diagrammatic expansion to both ascertain the validity of perturbation theory and to estimate quantitatively higher-order renormalization effects.
• While no direct signatures for non-Fermi liquid behavior at the Dirac point have yet been observed experimentally, there is ample evidence for the interaction-induced renormalization of the graphene velocity as the carrier density approaches zero.