Straightforward but simple evidence of non-Fermionic behavior of Dirac electrons in graphene is provided by the comparison of energy momentum dispersion of graphene on different dielectric substrate. Upon changing dielectric substrates, (i) the deviation from linearity is enhanced, resulting in the deformation of linear dispersion to a logarithmic one, and (ii) the dispersion becomes steeper approaching the strong electronic correlation limit (epsilon=1).

Resultanly, Fermi velocity, one of the key concepts in the study of a material, as it bears information on a variety of fundamental properties, is inversely proportional to the dielectric constant, providing a new venue to efficiently manipulate the important physical quantity. Furthermore, the fine structure constant of graphene is observed to be cloase to 1, which may indicate that a full theoretical treatment beyond the random-phase approaximation is required to understand this simple 2-dimensional system.