  Graphene exhibits unique material properties and in electromagnetic wave
technology, it raises the prospect of devices miniaturized down to the atomic
length scale. Here we study split-ring resonator metamaterials made from
graphene and we compare them to gold-based metamaterials. We find that
graphene's huge reactive response derived from its large kinetic inductance
allows for deeply subwavelength resonances, although its resonance strength is
reduced due to higher dissipative loss damping and smaller dipole coupling.
Nevertheless, tightly stacked graphene rings may provide for negative
permeability and the electric dipole resonance of graphene meta-atoms turns out
to be surprisingly strong. Based on these findings, we present a terahertz
modulator based on a metamaterial with a multi-layer stack of alternating
patterned graphene sheets separated by dielectric spacers. Neighbouring
graphene flakes are biased against each other, resulting in modulation depths
of over 75% at a transmission level of around 90%.
