  We demonstrate that graphene-based photonic superlattices provide a versatile
platform for electrical and all-optical control of photonic beams with
deep-subwavelength accuracy. Specifically, by inserting graphene sheets into
periodic metallo-dielectric structures one can design optical superlattices
that posses photonic Dirac points (DPs) at frequencies at which the spatial
average of the permittivity of the superlattice, $\bar{ \varepsilon}$,
vanishes. Similar to the well-known zero-$\bar{n}$ bandgaps, we show that these
zero-$\bar{\varepsilon}$ DPs are highly robust against structural disorder. We
also show that, by tuning the graphene permittivity via the optical Kerr effect
or electrical doping, one can induce a spectral variation of the DP exceeding
\SI{30}{\nano\meter}, at mid-IR and THz frequencies. The implications of this
wide tunability for the photonic Zitterbewegung effect in a vicinity of the DP
are explored too.
