The data labeled by the dashed (red) line correspond to λ = 10 − 2 in Eq. ( 16), while the data labeled by the solid (blue) line correspond to λ = 1. The vertical (black) line indicates the point k = k F. (in units of ε F) for monolayer graphene as a function of k / k F (for wave vectors up to the cut-off) for α e e = 0.5 and Λ = 10. Figure 1: (Color online) The pseudospin-dependent part of the Hartree-Fock self-energy Σ ( k ) We will mainly be interested in the contribution to the self-energy at k ∼ k F due toĮxchange interactions with states at k ′ ≫ k F, for ( α e e = e 2 / ϵ ℏ v is the graphene continuum-model fine structure constant.) Λ is a control parameter which can be adjusted to represent the weaker screening at higher frequencies. Where q T F = α e e k F is the Thomas-Fermi screening vector and
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