They have useful and unique electronic properties which are useful for probing new physics and they might be useful for spintronics and quantum computers. Those might be far faster forms of computing.

Electrons in monolayer graphene are described by massless Dirac electrons, which exhibit unique quantum phenomena due to the pseudospin and Berry phase of the massless electron.

A tunable bandgap up to 200 meV can be induced in bilayer graphene with electrical gating.

Dirac fermions in quasicrystalline graphene

Quasicrystal lattices, which can have rotational order but lack translational symmetry, can be used to explore electronic properties of materials between crystals and disordered solids. Ahn et al. grew graphene bilayers rotated exactly 30° that have 12-fold rotational order. Electron diffraction and microscopy confirmed the formation of quasicrystals, and angle-resolved photoemission spectroscopy revealed anomalous interlayer electronic coupling that was quasi-periodic.