Determine the true many-body electron interaction in graphene and related 2D materials

Determine the true many-body electron–electron interaction in monolayer graphene and other two-dimensional materials, specifying the microscopic interaction potential and its parameters beyond the phenomenological screened Coulomb form V(r) = (e^2/4π r)(1 − e^{-r/a}) employed in Pseudo Generalized QED (PGQED) with Podolsky parameter μ = 1/a.

Background

The paper introduces PGQED, a (2+1)D gauge-field theory obtained via dimensional reduction of Generalized QED (GQED), and uses its screened Coulomb potential V(r) ∝ (1 − e^{-r/a})/r to model electron–electron interactions with a Podolsky parameter μ = 1/a. In discussing applications to graphene, the authors estimate μ by matching experimental constraints on the possible band gap in the ultrarelativistic low-density regime.

While PGQED provides a tractable phenomenological framework, the authors explicitly note that the true many-body interaction among electrons in graphene and similar two-dimensional materials is not known. Resolving this would clarify the microscopic origin of screening effects and enable more definitive predictions about chiral symmetry breaking and gap generation in realistic systems.