Figure 3
From: Fermi velocity engineering in graphene by substrate modification
Fermi velocity and the strength of electron-electron interactions.
(A) E-ELDA dispersions for graphene on SiC(000-1) (blue line), BN (dark-yellow line) and quartz (red line). (B) Fermi velocities as a function of ε. The dashed line is a theoretical curve for vF, which is inversely proportional to ε6,23. Filled symbols correspond to experimental results, while empty symbols to theoretical values. ε = 2.45 for G/SiO226 is obtained from the standard approximation, ε = (εvacuum+εsubstrate)/2 (see text). (C) The ratio of vF, the renormalized Fermi velocity due to electron-electron interactions, to v0 = 0.85×106 m/s, the bare Fermi velocity in the LDA limit where ε = ∞4, as a function of α. The dashed line is the fit given by vF/v0 = 1-3.28 α{1+(1/4) ln[(1+4 α)/4 α]-1.45}31 for charge neutral graphene. The inset is the relation between α and ε, where the dashed line is 
23.
