Pressure and electric field dependence of quasicrystalline electronic states in 30° twisted bilayer graphene

A 30 degrees twisted bilayer graphene demonstrates the quasicrystalline electronic states with 12-fold symmetry. These states are, however, far away from the Fermi level, which makes conventional Dirac fermion behavior dominating the low-energy spectrum in this system. By using a tight-binding approximation, we study the effect of external pressure and electric field on the quasicrystalline electronic states. Our results show that, by applying the pressure perpendicular to the graphene plane, one can push the quasicrystalline electronic states towards the Fermi level. Then, the electron or hole doping on the order of similar to 4 x 10(14) cm(-2) is sufficient for the coincidence of the Fermi level with these quasicrystalline states. Moreover, our paper indicates that applying the electric field perpendicular to the graphene plane can destroy the 12-fold symmetry of these states, and it is easier to reach this in the conduction band than in the valence band. Importantly, the application of the pressure can partially recover the 12-fold symmetry of these states against the electric field. We propose a hybridization picture that can explain all these phenomena.