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

Abstract

30$^{\circ}$ 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 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 graphene plane one can push the quasicrystalline electronic states towards the Fermi level. Then, the electron or hole doping of the order of $\sim$ $4\times10^{14}$ $cm^{-2}$ is sufficient for the coincidence of the Fermi level with these quasicrystalline states. Moreover, our study indicates that applying the electric field perpendicular to the graphene plane can destroy the 12-fold symmetry of these states and break the energy degeneracy of the 12-wave states, and it is easier to reach this in the conduction band than in the valence band. Importantly, the application of the pressure can recover the 12-fold symmetry of these states to some extent against the electric field. We propose a hybridization picture which can explain all these phenomena.