Fig. 1.

Graphene photonic crystal. a Schematic of a photonic crystal comprised of a graphene monolayer fully-encapsulated by hexagonal boron nitride on top of an array of SiO₂ pillars. Inset, simulated carrier density map n_s(r) at average carrier density ${\overline{n}}_{\mathrm{s}}=4.5\times 10^{12}{\mathrm{cm}}^{-2}$, showing two hexagonal-patterned domains separated by an artificial lattice dislocation (domain wall). The lattice periodicity a = 80 nm. The photonic crystal unit cell is marked by a white dashed hexagon. b Calculated plasmonic band structure as a function of wave-vector k and average carrier density ${\overline{n}}_{\mathrm{s}}$. A vertical cut parallel to the $\omega -\mathbf{k}$ plane (back panel) generates the plasmonic band structure at fixed carrier density ${\overline{n}}_{\mathrm{s}}=5.5\times 10^{12}{\mathrm{cm}}^{-2}$. The dashed lines mark the range of a complete plasmonic bandgap. A horizontal cut parallel to ${\overline{n}}_{\mathrm{s}}-\mathbf{k}$ plane (bottom panel) generates the plasmonic dispersion as a function of average carrier density ${\overline{n}}_{\mathrm{s}}$ and wave-vector k, at laser frequency ω = 904 cm⁻¹; a complete bandgap is evident for carrier density around ${\overline{n}}_{\mathrm{s}}=5.5\times 10^{12}{\mathrm{cm}}^{-2}$