Left — graphene: electrons hop across a hexagonal carbon
lattice with almost no scattering, giving graphene its famous near-zero
band gap and extremely high conductivity, which strain can open up
slightly by distorting the lattice.
Right — metamaterial: a periodic array of sub-wavelength unit
cells gives the medium an effective negative refractive index at
certain frequencies, bending an incoming wavefront the "wrong" way.
σ_graphene ∝ n_electron / (1 + strain·k)
n_eff(ω) < 0 when ω is inside the metamaterial's resonance band
θ_refracted = −θ_incident · |n_eff| (negative refraction)
- Electron density — carrier concentration on the graphene sheet; more carriers, higher conductivity.
- Mechanical strain — stretching the lattice opens a small band gap and reduces conductivity.
- Wave frequency — determines whether the metamaterial cell array responds with positive or negative refraction.