It turns out that the energy density (J/m^{3}) of a capacitor with a dielectric can be expressed in a way that's independent of the capacitor geometry, and depends only on the dielectric properties, like so: C = ε_{0} ε_{r} A / d [Farad] U = 1/2 C v^{2} [Joule] V = A d [ m^{3} ] E_{0} = v_{0}/d [volt/m] (max field) so U/V = ε_{0}ε_{r} E_{0}^{2} [J/m^{3}]
So the critical field is the most important parameter, followed by the dielectric constant.
The linked article blurts "They exhibit a very high dielectric constant of 753". Er, no. A "high k" is found in stuff like BaTiO_{3} with k above 10,000. Therefore Fail.
Is the critical field specified? Buggered if I can find it. Therefore Fail.
The article is titled "Physicists develop graphene material for a more efficient energy storage." Only trouble is that we don't know what it is. King Useless.