Pressure and electric field dependence of quasicrystalline electronic states in 30${}^{\circ }$ 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 $\sim$ $4\times 10^{14}$ $c{m}^{-2}$ 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.

7 pages, 8 figures, 1 table

References in corpus (12)

• Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene
• Flat Bands in Slightly Twisted Bilayer Graphene
• Dependence of band structures on stacking and field in layered graphene
• Numerical studies of confined states in rotated bilayers of graphene
• Graphene under hydrostatic pressure
• Interlayer interaction in general incommensurate atomic layers
• Quasicrystalline electronic states in 30${}^{\circ }$ rotated twisted bilayer graphene
• 30${}^{\circ }$-twisted bilayer graphene quasicrystals from chemical vapor deposition
• Interlayer Decoupling in 30° Twisted Bilayer Graphene Quasicrystal
• Dodecagonal bilayer graphene quasicrystal and its approximants
• Band-unfolding approach to Moirè-induced band-gap opening and Fermi-level-velocity reduction in twisted bilayer graphene
• Emergent Localization in Dodecagonal Bilayer Quasicrystals

Cited by in corpus (9)

• Twistronics in graphene-based van der Waals structures
• Quasicrystalline electronic states in twisted bilayers and the effects of interlayer and sublattice symmetries
• Generalized Peierls substitution for the tight-binding model of twisted multilayer graphene in a magnetic field
• Interlayer hybridization in graphene quasicrystal and other bilayer graphene systems
• Quasiperiodic pairing in graphene quasicrystals
• Resonant interaction in chiral, Eshelby-twisted van der Waals atomic layers
• Quasicrystalline 30${}^{\circ }$ twisted bilayer graphene: Fractal patterns and electronic localization properties
• Trigonal Quasicrystalline States in $30^{\circ }$ Rotated Double Moiré Superlattices
• Magic angle and plasmon mode engineering in twisted trilayer graphene with pressure